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TRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂNTRẮC NGHIỆM CHUYÊN ĐỀ NGUYÊN HÀM TÍCH PHÂN
TRC NGHIM CHUYấN NGUYấN HM TCH PHN Đ1 NGUYấN HM Cõu 1: Trong cỏc khng nh sau, khng nh no sai: ự= f ( x ) dx A ũ ộ ũ g ( x )dx ờf ( x ) - g ( x ) dx ỷ ỳ ũ B F ( x ) = x l mt nguyờn hm ca f ( x ) = 2x C Nu F ( x ) v G ( x ) u l nguyờn hm ca hm s f ( x ) thỡ F ( x ) - G ( x ) = C (hng s) D F ( x ) = x l mt nguyờn hm ca f ( x ) = 2x Cõu 2: Hm s f ( x ) cú nguyờn hm trờn K nu: A f ( x ) xỏc nh trờn K B f ( x ) cú giỏ tr nh nht trờn K C f ( x ) liờn tc trờn K D f ( x ) cú giỏ tr ln nht trờn K Cõu 3: Mnh no sau õy sai: A Mi hm s liờn tc trờn ( a; b ) u cú nguyờn hm trờn ( a; b ) B F ( x ) l mt nguyờn hm ca f ( x ) trờn ( a; b ) F ' ( x ) = f ( x ) , " x ẻ ( a; b ) C ( ũ f ( x )dx ) ' = f ( x ) D Nu F ( x ) l mt nguyờn hm ca f ( x ) v C l mt hng s thỡ ũ f ( x )dx = F ( x ) + C Cõu 4: Trong cỏc khng nh sau, khng nh no sai: ' ự= f x A ộ f x dx ( ) ( ) ỳ ởũ ỷ B ũ f ( x ) dx = F ( x ) + C ị ũ f ( u ) dx = F ( u ) + C ũ k.f ( x ) dx = k ũ f ( x )dx ( k l hng s) D ũ f ( x ) dx = F ( x ) + C ị ũ f ( t ) dt = F ( t ) + C C Cõu 5: Xột hai khng nh sau: a; b ựu cú o hm trờn on ú (I) Mi hm s f ( x ) liờn tc trờn on ộ ỳ ỷ ựu cú nguyờn hm trờn on ú (II) Mi hm s f ( x ) liờn tc trờn on ộ ởa; b ỳ ỷ Trong hai khng nh trờn: A C hai ỳng B Ch cú (I) ỳng C C hai sai D Ch cú (II) ỳng ựnu: Cõu 6: Hm s F ( x ) c gi l nguyờn hm ca hm s f ( x ) trờn on ộ ờa; b ỳ ỷ A Vi mi x ẻ ( a; b ) , ta cú f ' ( x ) = F ( x ) ự, ta cú F ' ( x ) = f ( x ) B Vi mi x ẻ ộ ờa; b ỷ ỳ C Vi mi x ẻ ( a; b ) , ta cú F ' ( x ) = f ( x ) ( ) ( ) + D Vi mi x ẻ ( a; b ) , ta cú F ' ( x ) = f ( x ) v F ' a = f ( a ) v F ' b = f ( b ) Cõu 7: Xột hai cõu sau: (I) ũ ộờởf ( x ) + g ( x ) ựỳỷdx = ũ f ( x ) dx + ũ g ( x ) dx = F ( x ) + G ( x ) - C , vi F ( x ) , G ( x ) tng ng l mt nguyờn hm ca f ( x ) , g ( x ) , C l hng s (II) Mi nguyờn hm ca a.f ( x ) l tớch ca a vi mt nguyờn hm ca f ( x ) Trang 1/19 - Mó thi 132 Trong hai cõu trờn: A Ch cú (I) ỳng B Ch cú (II) ỳng C C hai cõu u sai D C hai cõu u ỳng Cõu 8: Trong cỏc cõu sau õy, núi v nguyờn hm ca mt hm s f xỏc nh trờn khong D , cõu no sai? (I) F l nguyờn hm ca f trờn D nu v ch nu " x ẻ D : F ' ( x ) = f ( x ) (II) Nu f liờn tc trờn D thỡ f cú nguyờn hm trờn D (III) Hai nguyờn hm trờn D ca cựng mt hm s thỡ sai khỏc mt hng s A Cõu (II) sai B Khụng cú cõu no sai C Cõu (I) sai D Cõu (III) sai Cõu 9: Hm s f ( x ) = A ( 0;p) cú nguyờn hm trờn: cos x ổ p pữ ữ ; ỗ B ỗ ữ ỗ ố 2ữ ứ ộ p pự - ; ỳ D ờ 2ỳ ỷ C ( p;2p) Cõu 10: Trong cỏc khng nh sau, khng nh no sai: u ' ( x) dx = log u ( x ) + C A ũ u ( x) B Nu F ( x ) l mt nguyờn hm ca hm s f ( x ) thỡ mi nguyờn hm ca hm s f ( x ) u cú dng F ( x ) + C , C l hng s C F ( x ) = + t an x l mt nguyờn hm ca hm s f ( x ) = a + t an x D F ( x ) = - cos x l mt nguyờn hm ca hm s f ( x ) = sin x Cõu 11: Trong cỏc khng nh sau, khng nh no sai: (vi C l hng s) xa+ A ũ 0dx = C B ũ x a dx = +C a+1 C ũ dx = ln x + C D ũ dx = x + C x NGUYấN HM C BN Cõu 12: Khng nh no sau õy sai: 1 A ũ cos 3x sin xdx = cos 4x - cos 2x + C 1ổ ữ +C ỗ- cos 4x - cos 2x ữ C ũ sin 3x cos x = ỗ ữ ữ 4ỗ ố ứ sin 5x + C 10 1ổ ữ ữ sin 3x + sin x +C ỗ D ũ cos 2x cos xdx = ỗ ữ ỗ ữ ố3 ứ B ũ sin xsinxdx = sin 3x - 3x + + sin 5x l nguyờn hm ca hm s no say õy: Cõu 13: Hm s F ( x ) = e 3x + ln + cos 5x A f ( x ) = 3e C f ( x ) = 3x + e - cos x + c 3x + - cos 5x B f ( x ) = ( 3x + 2) e 3x + + cos 5x D f ( x ) = 3e Cõu 14: Nguyờn hm ca hm s y = 3x - 5x + 2x - l: A y = 3x - 5x + x - 3x - C C y = 9x - 10x + - C x D y = x 4 B y = x + x - 3x - C x + 2x - 3x + C 3 Cõu 15: Hm s F ( x ) = e x l mt nguyờn hm ca hm s: Trang 2/19 - Mó thi 132 A f ( x ) = e ex B f ( x ) = 3x x3 C f ( x ) = 3x e x D f ( x ) = x e x -1 5x + - e- x + l nguyờn hm ca hm s no say õy: Cõu 16: Hm s F ( x ) = B f ( x ) = 35x + ln + e- x 5x + ln + e- x + C D f ( x ) = 5.3 5x + - e- x A f ( x ) = 5.3 5x + ln + e- x C f ( x ) = 5.3 ( ) x Cõu 17: Vi giỏ tr no ca a, b, c thỡ hm s F ( x ) = ax + bx + c e l nguyờn hm ca hm s ( ) y = x + x - ex A a = 1, b = 1, c = - B a = 1, b = - 1, c = C a = 1, b = 3, c = - D a = 1, b = - 1, c = Cõu 18: Nguyờn hm ca hm s f ( x ) = cot x - cot x l: A F ( x ) = - ln cos x + ln sin 3x + C C F ( x ) = ln s inx 2x Cõu 19: Cho I = ũ ln cos 3x + C 3 +C cos x cos2 3x + +C D F ( x ) = sin x sin 3x B F ( x ) = ln dx Khi ú kt qu no sai? x2 ổ1 ỗ2 2x + 2ữ ữ +C A I = ỗ ữ ỗ ữ ỗ ố ứ B I = 2x + C ổ1 ỗ2 2x - 2ữ ữ +C C I = ỗ ữ ỗ ữ ỗ ố ứ x3 x ũ f ( x )dx = + e + C thỡ f ( x ) bng: x4 x4 x A f ( x ) = 3x + e B f ( x ) = C f ( x ) = + ex + ex 12 D I = 2x + + C Cõu 20: Nu Cõu 21: Nu ũ f ( x )dx = - + ln x + C thỡ f ( x ) l: x2 + ln x + C x2 x- C f ( x ) = x A f ( x ) = - x D f ( x ) = x + e B f ( x ) = x + ln x + C D f ( x ) = - x+ +C x Cõu 22: F ( x ) l nguyờn hm ca hm s f ( x ) = ( 2x + 1) Chn ỏp ỏn sai 4x 4x B F ( x ) = + 2x + x - 5C + 2x + x + C 3 C F ( x ) = ( 2x + 3) + C D F ( x ) = x + x + C Cõu 23: Khng nh no sau õy ỳng: sin x + cos x A ũ dx = 4x + ln cos x + C cos x cos x dx = x - ln sin x + cos x + C B ũ sin x + cos x sin x + cos x C ũ dx = x + ln sin x + C sin x A F ( x ) = ( ) Trang 3/19 - Mó thi 132 D ũ cos x - sin x dx = + ln sin x + cos x + C sin x + cos x Cõu 24: Nguyờn hm ca hm s f ( x ) = 2.52x - + + 2x l: x 52x - 3- x 2x - + +C ln ln ln 52x - 3- x 2x C F ( x ) = - + +C ln ln ln 2x - ln - 2.3- x ln + x ln + C B F ( x ) = 4.5 A F ( x ) = D F ( x ) = 52x- 3- x 2x - + +C ln ln ln Cõu 25: Nguyờn hm ca hm s f ( x ) = ( x - 1) ( x + 1) l: x3 - x+ C ổx ửổ x2 ữ ữ ỗ ỗ ữ ữ F x = x + x +C ỗ D ( ) ỗ ữ ữ ỗ ỗ ữ ữ ỗ2 ỗ2 ố ứố ứ A F ( x ) = x - x + C B F ( x ) = C F ( x ) = 2x + C ũ e e x Cõu 26: Tớnh x+ dx ta c kt qu: A 2e2x + + C B Kt qu khỏc C 2x + e +C D e x ex + + C Cõu 27: Hm s no sau õy khụng phi l nguyờn hm ca f ( x ) = ( x - 3) : A F ( x ) = C F ( x ) = ( x - 3) ( x - 3) 5 D F ( x ) = - 2017 Cõu 28: Nguyờn hm ca hm s f ( x ) = A F ( x ) = B F ( x ) = + x B F ( x ) = +C ( 2x - 1) Cõu 29: Nu ũ f ( x ) dx = sin xcosx + C - p2016 ( x - 3) 5 2x + l: 2x - x+ +C x- C F ( x ) = - ( x - 3) - ( 2x - 1) D F ( x ) = x + +C ln 2x - + C thỡ f ( x ) l: ( cos x- cosx ) C f ( x ) = ( cos x + cos x ) Cõu 30: Khng nh no sau õy sai: A f ( x ) = ( cos 3x + cos x ) D f ( x ) = ( cos 3x - cos x ) B f ( x ) = ũ( - t an x ) dx = t an x + ln cos x + C B ũ ( cot x- t anx ) dx = t an x - cot x - 9x + C C ũ( sin x + cos x ) dx = x - cos 2x + C A 2 D ũ( - cot x ) dx = 3x - cot x + ln sin x + C Trang 4/19 - Mó thi 132 Cõu 31: Hm s F ( x ) = x + 5x - x + l nguyờn hm ca hm s no sau õy x5 x x2 + + 2x 4 C f ( x ) = 5x + 15x - B f ( x ) = 5x + 15x + A f ( x ) = D f ( x ) = x + 5x - Cõu 32: Khng nh no sau õy sai: A ũ ( 2x + 3) C ũ( x2 + dx = ( 2x + 3) 14 ) x dx = ( 2x + 3) 3 2 x x + x x+C + C B D ũ 1+ x x ũx ( x + dx = 33 x + x6 x + C ) x dx = 2 x x + x3 x + C f x = + ( ) Cõu 33: Nguyờn hm ca hm s 2x + ( 3x - 2) l: x A F ( x ) = x + 3x - 27 ( 3x - 2) C F ( x ) = ln 2x + - x B F ( x ) = x + 3x - +C +C 3x - D F ( x ) = 3x ( 3x - 2) +C 1 ln 2x + +C 3x - Cõu 34: Hm s F ( x ) = x + 5x - x + l nguyờn hm ca hm s no sau õy: A f ( x ) = x + 5x - C f ( x ) = B f ( x ) = 5x + 15x - x 5x x + + 2x 4 D f ( x ) = 5x + 15x + Cõu 35: Nguyờn hm ca hm s f ( x ) = x - 2x + l: x x2 B F ( x ) = - + C - 2x + ln x + C x 2 x - x + 3x x2 + C C F ( x ) = D F x = - 2x - + C ( ) x x Cõu 36: Khng nh no sau õy sai: 2x + dx = ln x - +C A ũ x- x - 4x + 2x + 11 dx = ln x - ln 3x - + C B ũ 2 3x - 4x + 2x dx = + +C C ũ x ( ) ( x - 3) ( x - 3) A F ( x ) = D 3 ũ ( x + 3) ( x + 1) dx = ln x+1 +C x+ Cõu 37: Nguyờn hm ca hm s y = A F ( x ) = ln x + ln ( x + 1) - + + l: x x+ x +C x B F ( x ) = ln x + ln ( x + 1) - +C x Trang 5/19 - Mó thi 132 C F ( x ) = - x - ( x + 1) - +C x D F ( x ) = ln x + ln x + - +C x 2x - + e- x + 3e x l: Cõu 38: Nguyờn hm ca hm s f ( x ) = 2e 2x- + e- x + 3e x + C A F ( x ) = 2e 2x - - e- x + 3e x + C B F ( x ) = 4e 2x - - e- x + 3e x + C C F ( x ) = e 2x - + e- x + 3e x + C D F ( x ) = e Cõu 39: Vi giỏ tr no ca m thỡ F ( x ) = mx + ( 2m + 1) x + l nguyờn hm ca hm s f ( x ) = 4x + A m = B m = C m = D m = Cõu 40: Nguyờn hm ca hm s f ( x ) = cos x + cos 3x + cos ( 2x + 1) l: A F ( x ) = - s inx - sin 3x - sin ( 2x + 1) + C C F ( x ) = - sin x - B F ( x ) = sin x + sin 3x + sin ( 2x + 1) + C 2 sin 3x - sin ( 2x + 1) + C D F ( x ) = sin x + sin 3x + sin ( 2x + 1) + C Cõu 41: Nguyờn hm ca hm s f ( x ) = s inx - sin 3x + sin ( 2x + 1) l: cos ( 2x + 1) + C C F ( x ) = - cos x + cos 3x - cos ( 2x + 1) + C B F ( x ) = cosx- cos x + cos ( 2x + 1) + C A F ( x ) = cos x - cos 3x + D F ( x ) = - cos x + cos 3x - cos ( 2x + 1) + C Cõu 42: Hm s F ( x ) = ln x + ln ( + cos x ) l nguyờn hm ca hm s no say õy: sin x + x + cos 3x sin 3x C f ( x ) = x + cos 3x sin x x + cos 3x sin 3x D f ( x ) = + cos 3x A f ( x ) = B f ( x ) = Cõu 43: Nguyờn hm ca hm s f ( x ) = t an x - t an 5x l: +C cos x cos2 5x D F ( x ) = ln sin x - ln sin x + C ln cos 5x + C 5 + +C C F ( x ) = sin x sin 5x Cõu 44: Khng nh no sau õy sai: B F ( x ) = A F ( x ) = - ln cosx + A ũ cot xdx = cot x- x + C C ũ t an 1ổ ữ ỗ ữ sin xdx = x sin 2x +C ỗ ữ ũ ữ 2ỗ ố ứ 1ổ ữ +C ỗx + sin 2x ữ D ũ cos xdx = ỗ ữ ữ 2ỗ ố ứ B xdx = t an x - x + C Cõu 45: Hm s no sau õy khụng phi l nguyờn hm ca hm s f ( x ) = A y = x2 - x + x- B y = x2 + x + x- Cõu 46: Mt nguyờn hm ca hm s f ( x ) = A x 3x 1 - 24 x 2x C y = ( x - 1) 4x x - 2x ( x - 1) x2 + x - x- D y = x2 x- l: B x 3x + ln x + 2x Trang 6/19 - Mó thi 132 C ( x - 1) D Kt qu khỏc 4x Cõu 47: Hm s F ( x ) = ln x + l nguyờn hm ca hm s no sau õy: A y = x B y = x+ C y = x ln x + 4x D y = + 5x + C x Cõu 48: Nguyờn hm ca hm s f ( x ) = ( sin x + cos x ) l: sin x + cos x ) + C ( 3 C ( sin x + cos x ) + C cos 2x + sin 2x + C D 5x + cos 2x - sin 2x + C A B 5x - Cõu 49: Nguyờn hm ca hm s f ( x ) = A ( x - 2) ( x + 3) ln ( x - 2) ( x + 3) + C C - x+ ln + C x- l: B x- ln +C x+ D x+ ln +C x- Cõu 50: Nguyờn hm ca hm s y = 3x + x - l: x2 - 3x + C D y = 6x + + C A y = 3x + x - 3x + C B y = x + C y = x + x - 3x + C Cõu 51: Nguyờn hm ca hm s f ( x ) = A F ( x ) = - ( x - 1) +C x - 2x + l: x- x2 F x = - x( ) B 2 ( x - 1) +C x2 D F ( x ) = ( x - 1) + ln x - + C - x + ln x - + C Cõu 52: Cp hm s no sau õy cú tớnh cht: Cú mt hm s l nguyờn hm ca hm s cũn li? x - x A f ( x ) = sin 2x, g ( x ) = cos x B f ( x ) = e , g ( x ) = e C F ( x ) = C f ( x ) = sin 2x, g ( x ) = sin x D f ( x ) = t an x, g ( x ) = cos2 x NGUYấN HM Cể IU KIN Cõu 53: Tỡm mt nguyờn hm ca hm s f ( x ) = 2ax + 5bx , bit F ( 1) = 2, F ( 2) = 1, F ( - 1) = 91 35 x - x 91 C F ( x ) = x - x - 10 A F ( x ) = Cõu 54: Cho hm s f ( x ) = A 95 96 91 x 91 D F ( x ) = x B F ( x ) = x - 2 x - 11 2- x F ( x ) l mt nguyờn hm ca f ( x ) tha F ( 1) = thỡ F ( 2) bng: Gi x5 97 31 B C D 96 32 Trang 7/19 - Mó thi 132 Cõu 55: Gi F ( x ) l mt nguyờn hm ca hm s f ( x ) = sin 2x tha F ( 0) = A B C ổ pử ữ ữ ỗ Tớnh F ỗ : ữ ỗ ữ ố ứ D 2 Cõu 56: Cho F ( x ) l mt nguyờn hm ca hm s f ( x ) = + 2x + 3x tha F ( 1) = Tớnh F ( 0) + F ( - 1) : A B - C - D Cõu 57: S thc m hm s F ( x ) = mx + ( 3m + 2) x - 4x + l mt nguyờn hm ca hm s f ( x ) = 3x + 10x - l: A m = B m = - D m = C m = Cõu 58: Cho hm s f ( x ) = + 2x Gi F ( x ) l mt nguyờn hm ca f ( x ) tha F ( 1) = thỡ: x2 A F ( x ) = + 6x 2 B F ( x ) = 3x + x + C F ( x ) = 2x + 3x + D F ( x ) = 3x + +2 x Cõu 59: Cho hm s f ( x ) = - 4x + x + 4x Gi F ( x ) l mt nguyờn hm ca f ( x ) tha F ( 0) = thỡ: x3 A F ( x ) = 2x - 2x + + x4 + x x4 C F ( x ) = - + 2x + x + +5 x2 x B F ( x ) = 2x + + x4 + 4 D F ( x ) = x - 2x + 3x + 2x + x x Cõu 60: F ( x ) = ( a cos x + b sin x ) e l mt nguyờn hm ca f ( x ) = e cos x thỡ giỏ tr ca a, b l: A a = 0, b = B a = 1, b = ( C a = b = D a = b = ) - x - x Cõu 61: Gi s hm s f ( x ) = ax + bx + c e l mt nguyờn hm ca hm s g ( x ) = x ( - x ) e Thỡ tng a + b + c bng: A - B C D ( ) x x Cõu 62: Cho hm s f ( x ) = x e Tỡm a, b, c F ( x ) = ax + bx + c e l mt nguyờn hm ca f ( x ) : A ( a; b; c) = ( - 1;2; 0) B ( a; b; c) = ( 1;2; 0) C ( a; b; c) = ( 1; - 2; 0) D ( a; b; c) = ( 2;1; 0) PHNG PHP I BIN S Cõu 63: Nguyờn hm ca y = x.e x A - x2 e +C B x2 e +C Cõu 64: Tỡm nguyờn hm F ( x ) = ũ sin C x2 e + ( ) 2 - ex ( ) x cos xdx sin x cos5 x sin x B F ( x ) = C F ( x ) = +C +C +C 5 Cõu 65: Cõu no sau dõy sai: A ũ f ( t ) dt = F ( t ) + C ị ũ f ( u ) du = F ( u ) + C, u = u ( x ) A F ( x ) = B D - D F ( x ) = cos x +C ũ f ( t )dt = F ( t ) + C ị ũ f ( u ( x ) ) u ' ( x ) dx = F ( u ( x ) ) + C Trang 8/19 - Mó thi 132 ( ) C Nu G ( t ) l mt nguyờn hm ca hm s g ( t ) thỡ G u ( x ) l mt nguyờn hm ca hm s ( ) g u ( x ) u ' ( x ) ( ) ( D Nu F ' ( t ) = f ( t ) thỡ F ' u ( x ) = f u ( x ) ) Cõu 66: Xột cỏc mnh sau: ũ t an xdx = - (I) (II) ũe (III) ũ cos x ln cos x + C sin xdx = - cos x + sin x sin x - cos x cos x e +C dx = sin x - cos x + C S mnh ỳng l: A B C Cõu 67: Nguyờn hm F ( x ) ca hm s y = ũ ln x +C x ln x C F ( x ) = - 2 A F ( x ) = D ln x dx tha F e = x ln x B F ( x ) = +2 x ln x D F ( x ) = + x+ C x ( ) e ln x ũ x dx theo phng phỏp i bin s, ta t: A t = eln x B t = C t = ln x x Cõu 69: Chn khng nh sai Cõu 68: tớnh A Nu F ( x ) , G ( x ) u l cỏc nguyờn hm ca hm s f ( x ) thỡ D t = x ũ ộởờF ( x ) - G ( x ) ựỷỳdx cú dng h ( x ) = Cx + D (C,D l cỏc hng s) B u ' ( x) ũ u ( x ) dx = u ( x) + C ũ f ( u ( x ) ) u ' ( x ) dx = F ( u ( x ) ) + C D F ( x ) = + sin x l mt nguyờn hm ca f ( x ) = sin 2x Cõu 70: F ( x ) l mt nguyờn hm ca y = e cos x Nu F ( p) = thỡ F(x) l: C Nu ũ f ( t ) dt = F ( t ) + C thỡ sinx A ecos x + B esin x + C C esin x + D e cos x + C Cõu 71: Tỡm nguyờn hm ca hm s f ( x ) = 2x - A ũ f ( x ) dx = ( 2x - 1) 2x - + C B ũ f ( x )dx = - C ũ f ( x ) dx = ( 2x - 1) 2x - + C D ũ f ( x )dx = 1 2x - + C 2x - + C NGUYấN HM TNG PHN Cõu 72: Mt nguyờn hm ca f ( x ) = x ln x l kt qu no sau õy, bit nguyờn hm ny triu tiờu x = Trang 9/19 - Mó thi 132 x ln x C F ( x ) = x ln x + A F ( x ) = x +1 x +1 ( ) ( B F ( x ) = ) x ln x + x + D Kt qu khỏc x Cõu 73: Hm s f ( x ) = ( x - 1) e cú mt nguyờn hm F ( x ) tha F ( x ) trit tiờu x = x A F ( x ) = ( x - 2) e + x B F ( x ) = ( x + 1) e + x C F ( x ) = ( x - 2) e x D F ( x ) = ( x - 1) e Cõu 74: Tớnh nguyờn hm F ( x ) = ũ ln ( ln x ) x dx A F ( x ) = ln x ln ( ln x ) + C B F ( x ) = ln x ln ( ln x ) - ln x + C C F ( x ) = ln x ln ( ln x ) + ln x + C D F ( x ) = ln ( ln x ) + ln x + C ũx Cõu 75: tớnh cos xdx theo phng phỏp tng phn, ta t: ỡù u = cos x ù A ùù dv = x dx ợ Cõu 76: Kt qu ỡù u = x ù B ùù dv = cos xdx ợ ỡù u = x ù C ùù dv = cos x ợ ỡù u = x ù D ùù dv = x cos xdx ợ x2 x e +C C e x + xe x + C D ũ xe dx x A xe x - ex + C B ũ x ln ( + x ) dx A u = x, dv = ln ( + x ) dx C u = x ln ( + x ) ; dv = dx Cõu 77: tớnh x2 x e + ex + C theo phng phỏp tng phn ta t: B u = ln ( + x ) ; dv = dx D u = ln ( + x ) , dv = xdx x Cõu 78: Tớnh nguyờn hm F ( x ) = ũ e s inxdx A F ( x ) = x e sin x - e x cos x + C ( ) x C F ( x ) = e cos x + C x B F ( x ) = e sin x + C D F ( x ) = x e sin x + e x cos x + C ( ) Đ2 TCH PHN Cõu 79: Mt ỏm vi trựng ngy th t cú s lng l N ( t ) Bit rng N ' ( t ) = cú 250000 Sau 10 ngy s lng vi trựng l (ly xp x hng n v): A 264334 B 257167 C 258959 4000 v lỳc u ỏm vi trựng + 0, 5t D 253584 13 t + v lỳc u bn khụng cú nc Tỡm mc nc bn sau bm nc c giõy (lm trũn kt qu n hng phn trm) A 2,66 m B 5,06 m C 2,33 m D 3,33 m Cõu 81: Hóy chn mnh sai: a a -ở a; a ự A Hm s f ( x ) liờn tc trờn ộ thỡ f x dx = ( ) ỳ ũ0 f ( x )dx ỷ ũ- a Cõu 80: Gi h ( t ) l mc nc bn cha sau bm nc c t giõy Bit rng h ' ( t ) = B ũ x dx ũ x dx Trang 10/19 - Mó thi 132 x dt l F ' ( x ) = 1+ t 1+ x b f ( x ) dx + C o hm ca hm s F ( x ) = ũ D Nu f ( x ) liờn tc trờn Ă thỡ Cõu 82: Cho tớch phõn I = ũ ũ a ( x - 2) ( x b c f ( x ) dx = ũ f ( x ) dx a ) dx = a + b ln + c ln - x+ x+ ỳng: A b > ũ c ( x > 0) B a < C c > , ( a, b, c ẻ Ô ) Chn khng nh D a + b + c > Cõu 83: Tớnh cỏc hng s A v B hm s f ( x ) = A sin ( px ) + B tha ng thi cỏc iu kin f ' ( 1) = v A A = ũ f ( x )dx = ;B = - p Cõu 84: Cho ;B = - p B A = - ũ f ( x )dx = 10 Khi ú ũ A 32 B 34 Cõu 85: Giỏ tr no ca b Cõu 86: Cho ũ D A = - ;B = p D 40 b ũ ( 2x - 6) dx = f ( x ) dx = v A 2 ;B = p ộ2 - 4f ( x ) ựdx bng: ỳ ỷ C 36 B b = 1; b = A b = 0, b = C A = ũ C b = 5, b = f ( t ) dt = - Giỏ tr B - ũ f ( u ) du D b = 0, b = bng: C D - ự Hóy chn mnh sai di õy: Cõu 87: Cho hm s f ( x ) liờn tc trờn on ộ ờa; b ỳ ỷ A B ũ b a ũ a f ( x ) dx = ũ f ( - x ) dx b b a kdx = k ( b - a ) , " k ẻ Ă b a ũ f ( x )dx = - ũ f ( x )dx D ũ f ( x ) dx = ũ f ( x ) dx + ũ f ( x ) dx, C a b b c a Cõu 88: Cho bit A C ũ ũ b a c f ( x ) dx = - 2; ũ ự "c ẻ ộ ởa; b ỳ ỷ f ( x ) dx = 3; ũ g ( x )dx = Chn ng thc sai: B ũ ộ f x + g( x) ự = 10 ỳ ở( ) ỷ ộ4f ( x ) - 2g ( x ) ựdx = - ỳ ỷ ũ f ( x )dx = - D ũ f ( x )dx = t2 + ( m / s) Quóng ng vt ú i c t+ giõy u tiờn bng bao nhiờu? (Lm trũn kt qu n hng phn trm) A 18, 82 m B 4, 06 m C 11, 81m D 7, 28 m Cõu 89: Mt vt chuyn ng vi tc v ( t ) = 1, + Cõu 90: Nu f ( 1) = 12, f ' ( x ) liờn tc v A B 29 ũ f ( x )dx = 17 Giỏ tr f ( 4) C l: D 19 ( ) 2 Cõu 91: Mt vt ang chuyn ng vi tc 10m/s thỡ tng tc vi gia tc a ( t ) = 3t + t m / s Quóng ng vt i c khong 10 giõy k t bt u tng tc bng bao nhiờu? Trang 11/19 - Mó thi 132 A 4000 m Cõu 92: Nu B ũ A c = 81 2200 m C 4003 m dx = ln c vi c ẻ Ô thỡ giỏ tr ca c l: 2x - B x = C c = x D 1900 m D c = ựl: Cõu 93: Cho F ( x ) = ũ t + t dt Giỏ tr nh nht ca hm s F ( x ) trờn on ộ ở- 1;1ỳ ỷ ( ) A Cõu 94: B k ũ (k- C D - 4x ) dx = - 5k thỡ giỏ tr k l: A k = B k = C k = D k = dx a = ln vi a, b ẻ Ơ v c chung ln nht ca a v b bng Chn khng x + b nh sai cỏc khng nh sau: A a - b > B a + 2b = 13 C 3a - b < 12 D a + b = 41 Cõu 95: Nu kt qu ca ũ x+1 dx vi a > Khi ú giỏ tr ca a l: x e A B e2 C D e e 2ổ 1ử ữ - 2ữ dx ta thu c kt qu dng a + b ln ci a, b ẻ Ô Chn ỗ Cõu 97: Tớnh tớch phõn ũ ỗ ữ ỗ ữ ốx - x x ứ Cõu 96: Cho ũ a khng nh ỳng cỏc khng nh sau: A a + b > 10 B a - b > C a > D b - 2a > Cõu 98: Mt ụ tụ ang chy vi tc 10m / s thỡ ngi lỏi p phanh; t thi im ú, ụ tụ chuyn ng chm dn u vi tc v ( t ) = - 5t + 10 ( m / s) , ú t l thi gian tớnh bng giõy, k t lỳc bt u p phanh Hi t lỳc p phanh n ụ tụ dng hn, ụ tụ cũn chuyn ng c bao nhiờu một? A 10m B 36m C 2m D 20m xổ 1ữ ữ sin t dt = vi k ẻ Â thỡ x tha: ỗ Cõu 99: ũ ỗ ỗ ữ 2ữ ố ứ A x = k2p B x = k p ổ ỗ ỗx + + - 1ỗ xố ũ Cõu 100: Kt qu ca tớch phõn a + b bng: A Cõu 101: Bit rng B ũ A a + b < 0 p D x = ( 2k + 1) p ữ ữ dx c vit di dng a + b ln vi a, b ẻ Ô Khi ú ữ ữ 1ứ C D - 2x + dx = a ln + b vi a, b ẻ Ô Khng nh no sau õy sai: 2- x B a < C b > D a + b > 30 Cõu 102: Cho tớch phõn I = ỳng: A a + b + c > C x = k ũ (x B b > ) - 2x ( x - 1) 2- x dx = a + b ln + c ln 3, ( a, b, c ẻ Ô ) Chn khng nh C c < D a < Trang 12/19 - Mó thi 132 Cõu 103: Mt vt chuyn ng vi tc v ( t ) ( m / s) ,cú gia tc v ' ( t ) = m / s2 Vn tc ban u t+1 ( ca vt l 6m/s Vn tc sau 10 giõy l (lm trũn kt qu n hng n v): A 12 m/s B 13 m/s C 11 m/s Cõu 104: Nu a ũ ( sin x + cos x ) dx = ( < a < 2p) ) D 14 m/s thỡ giỏ tr ca a bng: p 3p p B C D p 2 Cõu 105: Gi s hm s f ( x ) liờn tc trờn khong K v a, b ẻ K , ngoi k l mt s thc tựy ý Khi ú A (I) a ũ f ( x ) dx = (II) a b a ũ f ( x )dx = ũ f ( x )dx a ũ (III) b a b b k.f ( x ) dx = k ũ f ( x ) dx a Trong mnh trờn: A Ch cú (II) sai B Ch cú (I) v (II) sai C Ch cú (I) sai D C ba u ỳng Cõu 106: Bn Nam ang ngi trờn mỏy bay i du lch th gii v tc chuyn ng ca mỏy bay l v ( t ) = 3t + ( m / s) Quóng ng mỏy bay i c t giõy th n giõy th 10 l: A 252 m B 36 m C 966 m Cõu 107: Trong cỏc khng nh sau, khng nh no ỳng? A ũ b a b f1 ( x ) f2 ( x ) dx = ũ f1 ( x ) dx.ũ f2 ( x )dx a B Nu C b D 1134 m ũ - a a ũ f ( x ) dx = thỡ f ( x ) l hm s l dx = D Nu f ( x ) liờn tc v khụng õm trờn on Cõu 108: Cho bit ũ ộ3f ( x ) + 2g ( x ) ựdx = v ỳ ỷ A B - Cõu 109: Cho d ộa; b ựthỡ ỳ ỷ hm d ũ b ũ f ( x )dx a ộ2f ( x ) - g ( x ) ựdx = - Giỏ tr ỳ ỷ C f D liờn tc trờn c ũ f ( x )dx 1 Ă tha c ũ f ( x )dx = 10, ũ f ( x )dx = 8, ũ f ( x )dx = ( a < b < c < d ) Khi ú ũ f ( x ) dx a b A - a C Cõu 110: Cho f ( x ) l hm s chn v A ũ f ( x )dx = a bng: b B bng: D - ũ f ( x )dx = a Chn mnh ỳng: B ũ f ( x ) dx = C ũ f ( x ) dx = 2a - 3 - - Cõu 111: Gi s A,B l cỏc hng s ca hm s f ( x ) = A sin ( px ) + Bx , bit D ũ f ( x )dx = - a ũ f ( x ) dx = Giỏ tr ca B l: A B C D ỏp ỏn khỏc I BIN S LOI Cõu 112: i bin s x = sin t ca tớch phõn I = ũ A I = ũ p ( - cos 2t ) dt 16 - x dx , ta c: p B I = 16 cos2 t dt ũ Trang 13/19 - Mó thi 132 p p D I = ( + cos 2t ) dt ũ C I = - 16 cos2 t dt ũ 0 Cõu 113: i bin s x = t an t ca tớch phõn I = A I = p p 3 ũ dt Cõu 114: Cho tớch phõn I = p ũ dx ũ t dt ũ C I = D I = ũp3 dt D I = ũ p dt t x2 - ta c: dx Nu i bin s x = sin t x p p B I = ũ cos t dt ũ (1- ũ p dt t A I = ũ cos t dt p p p p C I = dt ũ Cõu 115: Cho tớch phõn I = 3 C I = p B I = dt ũ dx ta c: x + Nu i bin s x = sin t ta c: - x2 p A I = t dt ũ p p p p 3 B I = ũ cos t ) dt p p ũ D I = sin t dt I BIN S LOI Cõu 116: Cho tớch phõn I = ũ + x2 dx Nu i bin s t = x2 A I = ũ t2 dt t2 + B I = - Cõu 117: Cho f ( x ) l hm s l v A ũ ũ - t dt t +1 C I = - f ( x ) dx = Giỏ tr B x + thỡ: x ũ t2 dt t2 - ũ f ( x )dx D I = ũ t2 dt t2 - l: C - D Cõu 118: Cho hm s f ( x ) cú nguyờn hm trờn Ă Mnh no di õy ỳng: A C p p ũ f ( s inx ) dx = pũ f ( s inx ) dx ũ B f ( x ) dx = ũ f ( - x ) dx D Cõu 119: Bin i I = ũ ln x e x ( ln x + 2) dx thnh I = 1 ũ a - a a f ( x ) dx = ũ f ( x ) dx ũ f ( t )dt 2 ũ f ( x ) dx = ũ f ( x ) dx vi t = ln x + Khi ú f ( t ) l hm s no sau õy: A f ( t ) = t2 t B f ( t ) = - Cõu 120: Bin i ũ0 hm s sau: A f ( t ) = t + t x 1+ 1+ x + t t2 dx thnh ũ f ( t ) dt B f ( t ) = t - t C f ( t ) = - + t t D f ( t ) = + t t2 , vi t = + x Khi ú f ( t ) l hm s no cỏc C f ( t ) = 2t - 2t D f ( t ) = 2t + 2t p Cõu 121: Nu I = sin n x cos xdx = thỡ n bng: ũ 64 Trang 14/19 - Mó thi 132 A n = B n = A - 4x ũ Cõu 122: Cho 3m - (x ) +2 C n = dx = Khi ú 144m - bng: C 3 B - ũ Cõu 123: Bin i I = ln t2 - A f ( t ) = dx thnh I = x e +1 B f ( t ) = t + t p D n - ũ f ( t )dt D Kt qu khỏc vi t = e x Khi ú f ( t ) l hm s no sau õy 1 + t t+1 C f ( t ) = 1 t+1 t D f ( t ) = Cõu 124: Cho tớch phõn I = esin x sinxcos xdx Nu i bin s t = sin x thỡ: ũ A I = e t ( - t ) dt ũ0 1 ( B I = ũ e t ( - t ) dt ) C I = ũ e t + t e t dt D I = Cõu 125: i bin s u = ln x thỡ tớch phõn I = A I = ũ ( - u ) e u du B I = ũ e 1 ũ ( - u ) du ự ũ t e dt ỳỳỷ t - ln x dx tr thnh: x C I = 1ộ t ờũ e dt + 2ờ ở0 ũ ( - u) e 2u D I = ũ ( - u ) e- u du du Cõu 126: Cho I = ũ 2x x - 1dx v u = x - Chn khng nh sai: 23 A I = u 3 B I = ũ p Cõu 127: Bin i ũe sin 2xdx thnh t A f ( t ) = e sin 2t ũ f ( t ) dt t B f ( t ) = e udu ú giỏ tr ca a bng: A a = B a = - vi t = sin x Khi ú f ( t ) l hm s no sau õy: t C f ( t ) = e sin t dx Cõu 128: Kt qu ca tớch phõn I = ũ1 x + x2 D f ( t ) = cú dng I = a ln + b ln C a = ( t e ) - + c vi a, b, c ẻ Ô Khi D a = - e x dx ae + e = ln vi a,b l cỏc s nguyờn dng - + ex ae + b B a = C a = D a = Cõu 129: Tỡm a bit I = ũ Cõu 130: Cho f ( x ) l hm s chn v A Cõu 131: Tớnh tớch phõn I = A I = e sin x p A a = D I = ũ C I = udu ũ - B ũ x.e B I = f ( x ) dx = Giỏ tr ũ f ( x ) dx - C x2 bng: D - dx e+ C I = e D I = e- Trang 15/19 - Mó thi 132 Cõu 132: Cho I = A I = ũ ũ + ln x dx v t = + ln x Chn khng nh sai: x e 2 t dt 2 C I = t 2 B I = ũ t dt D I = 14 D I = n p Cõu 133: Tớnh tớch phõn I = ( - cos x ) n sin xdx ũ n+1 A I = B I = 1- n Cõu 134: Kt qu ca tớch phõn I = ũ1 sau õy ỳng: A a + b = ln x e ( ) x ln x + 1 B a = ũ ln D 2a + b = C a - b = x dx = ln a, a ẻ Ă Khi ú giỏ tr ca a bng: x +1 Cõu 136: Cho I = 2n dx cú dng I = a ln + b, ( a, b ẻ Ô ) Khng nh no B ab = Cõu 135: Bit rng I = ũ A a = C I = C a = D a = e x e x - 1dx v t = e x - Chn khng nh sai: A I = t 3 B I = ũ 2t 2dt C I = D I = C I = 52 D I = - C I = 15 D I = ũ t dt 2 Cõu 137: Tớnh tớch phõn I = ũ x x + 1dx A I = 19 16 B p ( ) 52 Cõu 138: Tớnh tớch phõn I = sin x + sin x dx ũ A I = 31 B I = p4 64 ự Mnh no sau õy ỳng: Cõu 139: Cho f ( x ) l hm s l v liờn tc trờn ộ ở- a;a ỳ ỷ A C ũ a - a f ( x ) dx = ũ f ( x ) dx a B - a a ũ f ( x ) dx = 2ũ f ( x )dx - a Cõu 140: Tớnh tớch phõn I = A I = ln D ũ ũ a - a a f ( x ) dx = - ũ f ( x ) dx a ũ f ( x )dx = - a ln x dx x B I = C I = ln 2 D I = - ln 2 D I = - p Cõu 141: Tớnh tớch phõn I = ũ cos x sin xdx A I = B I = - p4 C I = - p Trang 16/19 - Mó thi 132 TCH PHN TNG PHN Cõu 142: Bit I = ũ a A a = ln x 1 dx = - ln Giỏ tr ca a bng: 2 x B a = ln C a = p p x x Cõu 143: Cho I = ũ e cos xdx, J = ũ e sin xdx, K = D p ũe x cos 2xdx Khng nh no sau õy ỳng cỏc khng nh sau: (I) I + J = ep (II) I - J = K A C (II) v (III) (III) K = B Ch (I) C Ch (II) ep - D Ch (III) Cõu 144: Cho I n = A enx ũ + ex dx ( n ẻ Ơ ) Giỏ tr I + I1 l: B C Cõu 145: Tớch phõn I = ũ A ( x - 1) e 2x dx = B D 3 - e2 Giỏ tr a > bng: C D Cõu 146: Cho I = ũ ( 2x + 3) e x dx = ae + b ( a, b ẻ Ô ) Chn khng nh ỳng: A ab = B a + b = 28 Cõu 147: Kt qu ca tớch phõn I = a - b bng: A - ũ ln ( x C a - b = 2 D a + 2b = ( a, b ẻ Â ) Khi ú ) - x dx c vit di dng a ln - b C B D e Cõu 148: Tớnh tớch phõn I = ũ x ln xdx A I = e +1 B I = Cõu 149: Cho tớch phõn I = C I = p ũ x ( s inx + 2m ) dx = + p e2 - 2 D I = e2 - Giỏ tr ca m l: A B t Cõu 150: Vi t ẻ ( - 1;1) ta cú ũx A - B Cõu 151: Tớnh tớch phõn I = A I = Cõu 152: Cho m A 30 ũ dx = - ln Khi ú giỏ tr ca t bng: - p D C C D x sin xdx B I = p ũ x cos xdx = Khi ú 9m C I = p D I = - bng: B C - D - 30 Trang 17/19 - Mó thi 132 p ổ p 1ử ữ - Khng nh no ỗ - ữ Cõu 153: Kt qu tớch phõn I = ( 2x - - sin x ) dx c vit di dng p ỗ ữ ữ ỗ ũ ốa b ứ sau õy sai: A a - b = B a + 2b = C a + b = Cõu 154: Khng nh no sau õy ỳng v kt qu I = A a - b = B ab = 64 Cõu 155: Kt qu tớch phõn I = a + b + c bng: A x ln xdx = 3ea + b C a - b = 12 ũ x ln ( + x ) dx D ab = 46 c vit di dng I = a ln + b ln + c Khi ú tng B Cõu 156: Cho tớch phõn I = ũ e D 2a - 3b = D C p ũ sin 2x.e s inx dx Mt hc sinh gii nh sau: Bc t t = s inx ị dt = cos xdx ỡù x = ị t = ùù ị I = ũ t.e t dt i cn: p ùù x = ị t = ùùợ ỡù u = t ị du = dt ù Bc Chn ùù dv = e t dt ị v = e t + ợ Suy ( ) 1 ũ t e dt = e + t t t 0 ũ( e t ) ( ) ( + dt = e t + t - e t + t 0 ) =1 Bc I = 2.1 = Hi bi gii trờn ỳng hay sai? Nu sai thỡ sai õu? A Bi gii hon ton ỳng B Bi gii sai t Bc C Bi gii sai t Bc D Bi gii sai t Bc Cõu 157: Tớnh tớch phõn I = ũ x.2 x dx A I = ln + B I = e ln + ln 2 k Cõu 158: Cho I = ũ ln x dx Xỏc nh k I < e - A k < e - B k > e + 1 C I = ln - ln D I = ln - ln 2 C k < e D k < e + 2 Cõu 159: Tớnh tớch phõn I = ũ ln t dt Khng nh no sau õy sai: A I = ln 4e B I = ln - log10 C I = ln - D I = ln e - - HT Trang 18/19 - Mó thi 132 CU 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 P N D C B B D D D B B A B A A B C C D C B D C D D A B C A D C D C D D B A C B C B A CU 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 P N A C D A B D A B D B C C A C D C A B A C B C A A D D B C B C C D A B B A D A A A CU 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 P N A C D B B D A D C B C D D A A D B C C A A A B B A C D B B C B D A B B C C C B C CU 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 P N A A B A D B B D D C D B A D B D C C D C A A A C A D D A B C A A C B D A D C A Trang 19/19 - Mó thi 132