Đây là tài liệu được viết dưới dạng câu hỏi trắc nghiệm gồm hơn 200 câu hỏi. Tài liệu được viết với 3 phần Nguyên Hàm Tích Phân Ứng dụng của tích phân.Đây là tài liệu giúp các em ôn tập củng cố kỹ năng tính nguyên hàm tích phân và ứng dụng 1 cách nhanh nhất.
CHUYấN TCH PHN ễN TP :NGUYấN HM- TCH PHN - NG DNG 100 CU TRC NGHIM V NGUYấN HM- TCH PHN - NG DNG A PH N NGUYấN HM LUYN TP GT 12 CHNG IV (16-17) NGUYấN HM Cõu 1: Tỡm x x + 1dx (x + 1) + C C (x + 1) x + + C Cõu 2: Tỡm sin x.cos x dx A A sin3 x + C B B Cõu 3: Tỡm (2x + 1) ln x dx sin x + C C x2 x+C x2 C (x2 + x) ln x + x + C (x + 1) x + + C D cos3 x + C B (x2 + x) ln x xdx x +C Cõu 5: Tỡm nguyờn hm ca hm s f(x) = sin x A cos3 x + C D x2 x+C x2 D (x2 + x) ln x + x + C A (x x) ln x Cõu 4: Tỡm 33 x +1 + C x +C B 1 1 C f(x)dx = x sin 2x + C 2 A f(x)dx = x + sin 2x + C C x x +C D x x +C B f(x)dx = x sin 2x + C D f(x)dx = sin 2x + C Cõu 6: Tỡm nguyờn hm ca hm s f(x) = cos x.cos3x 1 C f(x)dx = cos 4x + cos 2x + C sin 2x dx Cõu 7: Tỡm cos2 x A ln sin x + C B ln cos x + C A f(x)dx = sin 4x sin 2x + C 1 B f(x)dx = sin 4x + sin 2x + C D f(x)dx = sin 4x sin 2x + C C ln sin x + C D ln cos x + C x + 2x dx Cõu 8: Tỡm (x + 1)e A 2(x + 1)ex + 2x +C B x2 + 2x e +C 2 C e x +2x + C D Cõu 9: Tỡm e2x e2x + 2dx A GV 2x (e + 2) + C B (x + 1)e x + 2x + C 2x (e + 2) e2x + 2) + C CHUYấN TCH PHN C 2x e +2 +C D Cõu 10: Tỡm nguyờn hm ca hm s f(x) = 3x A f(x)dx = ln + + C x C f(x)dx = 3x ln + + C x ln x Cõu 11: Tỡm dx x 1 1 A ln x + + C B ln x + + C x x x x (2 + 3ln x) dx Cõu 12: Tỡm x A (2 + ln x)3 + C B (2 + ln x)3 + C x2 3x + +C B f(x)dx = ln x 3x +C D f(x)dx = ln x x Cõu 13: Tỡm nguyờn hm ca hm s y = f(x) = tan(2x 1) + C Cõu 14: Tỡm tan 2x dx A A ln cos 2x + C ln cos 2x + C A f(x)dx = 2e + x + C x f(x)dx = 2xe x f(x)dx = 3x cos x + C 1 ln x + C x x D ln x + C x x C (2 + 3ln x)3 + C D (2 + 3ln x)3 + C cos (2x 1) x Cõu 15: Tỡm nguyờn hm ca hm s f(x) = 2e + C C B tan(2x 1) + C B 2x (e + 2) e2x + + C + x +C C tan(2x 1) + C D cot(2x 1) + C C ln cos 2x + C D ln sin 2x + C x f(x)dx = 2e + x + C D f(x)dx = e + x + C x B 2x Cõu 16: Tỡm nguyờn hm ca hm s f(x) = x 2sin x A 2 C f(x)dx = 3x + cos x + C Cõu 17: Nguyờn hm ca hm s f(x) = x cos x l: A x cos x + sin x + C B x sin x + cos x + C Cõu 18: Tỡm 3(x + ln 2x)xdx 3x ln x x + C 3x ln x + x + C C x3 2sin x dx Cõu 19: Tỡm 3cos x + A x3 + GV D f(x)dx = x + cos x + C B f(x)dx = x cos x + C C x sin x + cos x + C 3x ln x x2 + C 3x ln x + x + C D x3 + B x3 D x sin x cos x + C CHUYấN TCH PHN A ln 3cos x + + C B ln 3cos x + + C C ln cos x + + C Cõu 20: Tỡm x x + 2dx A (x + 2) + C B D ln 3cos x + + C (x + 2) + C Cõu 21: Tỡm nguyờn hm ca hm s f(x) = C 2 (x + 2) x + + C D x +2 +C 3 sin x A f(x)dx = cot x 3x + C f(x)dx = tan x 3x + C f(x)dx = cot x 3x + C B C f(x)dx = tan x 3x + C D Cõu 22: Tỡm nguyờn hm ca hm s f(x) = cos x sin x A cos2x + C B cos2 x sin x + C Cõu 23: Tỡm nguyờn hm ca hm s f(x) = tan x + C dx Cõu 24: Tỡm nguyờn hm I = 2016x ln x A 2016 ln x + C B +C 2016 3x Cõu 25: Tỡm (x + 1)e dx A co t x + C C cot x + C C 1 (x + 1)e3x e3x + C 3 C (x + 1)e3x e3x + C x x Cõu 26: Tỡm nguyờn hm I = e (2x + e )dx A C 2xe x 2e x + e 2x + C ln x e dx Cõu 27: Tỡm x eln x +C A B eln x + C x A 2xe x + 2e x e2x + C A x + ln x + + C B ln 2016x 4032 sin 2x + C +C D tan x + C D 2016 ln 2016x + C 1 (x + 1)e3x + e3x + C 1 D (x + 1)e3x e3x + C B D 2xex 2e x e 2x + C B 2xe x + 2ex + e2x + C C eln x + C D eln 2x + C C x ln x + + C D x ln x + + C x l: x+2 +C (x + 2)2 + ln x dx Cõu 29: Tỡm x GV D 1 cos2x B Cõu 28: Nguyờn hm ca hm s f(x) = C sin 2x + C CHUYấN TCH PHN A ln x + ln3 x + C Cõu 30: Tỡm C ln x + ln3 x + C B ln x + ln x + C cos x dx x sin +C sin x Cõu 31: Tỡm nguyờn hm ca hm s f(x) = cos2 x A +C cos2 x B 2 A f(x)dx = x + sin 2x + C C D + ln x + C B f(x)dx = sin 2x + C Cõu 32: Cho hm s f(x) = +C sin2 x D 1 +C sin x f(x)dx = x + sin 2x + C D f(x)dx = x sin 2x + C Tỡm nguyờn hm F(x) ca hm s f(x), bit F( ) = (x 3)2 3x 10 x2 3x C F(x) = D F(x) = x x3 x3 f(x) = (3x + 1)sin x Cõu 33: Nguyờn hm ca hm s l: (3x + 1) cos x 3sin x + C A B (3x + 1) cos x 3sin x + C C (3x + 1) cos x + 3sin x + C D (3x + 1) cos x + 3sin x + C A F(x) = +C x C B F(x) = Cõu 34: Tỡm (1 + sin x) cos x dx (1 + sin x)4 + C 2x Cõu 35: Tỡm 3xe dx A A 3xe2x e2x + C Cõu 36: Tỡm 3x x2 + C (1 + sin x)4 + C D 2x 2x xe e + C C 2x 2x xe + e + C D 3xe2x 3e2x + C B B 1 x sin 2x + sin 4x + C 32 1 C x sin 2x + sin 4x + C 8 Cõu 38: Tỡm nguyờn hm I = B x dx sin x A x cot x + ln cos x + C B x cot x ln sin x + C C x cot x + ln sin x + C D x cot x + ln sin x + C Cõu 39: Tỡm nguyờn hm ca hm s f(x) = D 1 x + sin 2x sin 4x + C 32 1 D x + sin 2x sin 4x + C 8 A GV (1 + sin x)4 + C dx 93 (x + 1)2 + C C x + + C 4 Cõu 37: Tỡm nguyờn hm ca hm s y = f(x) = sin x A 43 (x + 1)2 + C B (1 + sin x)4 + C 5x + 7x 33 (x + 1)2 + C CHUYấN TCH PHN x x 5 ữ A + C ln x 25 ữ +C B ln x 25 ữ +C C ln 5 25 ữ +C D ln C ln(e x + 1) + C D ex Cõu 40: Tỡm x dx e +1 B ln A ex + + C x Cõu 41: Tỡm x(3 + 2e )dx ex +C ex + 3x 2xe x + 2e x + C 3x + 2xex + 2e x + C C 3x + 2xe x 2e x + C 3x 2xe x 2ex + C D A Cõu 42: Cho hm s f(x) = B Tỡm nguyờn hm F(x) ca hm s f(x), bit F( ) = x(x + 1) A F(x) = ln x ln x + + C C F(x) = ln B F(x) = ln x ln x + + ln x +1 ln x D F(x) = ln 3x Cõu 43: Tỡm x dx 2.3 + x ln(2.3 + 1) +C A ln x (e + 1) + C B ln(2.3x + 1) +C C x ln x +1 ln(2.3x + 1) +C ln D cos 2x sin x + cos x B sin x + cos x + C C cos x sin x + C ln(2.3x + 1) +C ln Cõu 44: Tỡm nguyờn hm ca hm s f(x) = A sin x cos x + C Cõu 45: Tỡm A 3dx x(2 + ln x) +C 2(2 + ln x)2 B +C (2 + 3ln x)2 C +C 2(2 + ln x)2 D +C 2(2 + ln x)2 C cos2x e +C D sin2x e +C cos2x Cõu 46: Tỡm e sin 2xdx A ecos2x + C D sin 2x + C B ecos2x + C Cõu 47: Nguyờn hm ca hm s f(x) = (2x 3) cos2x l: 1 (2x 3)sin 2x cos 2x + C 2 1 C (2x 3) cos 2x + sin 2x + C 2 A Cõu 48: Tỡm nguyờn hm ca hm s y = f(x) = A GV +C (2 x)2 B +C 2(2 x)2 2 B (2x 3)sin 2x + cos 2x + C D 1 (2x 3)sin 2x + cos 2x + C 2 (2 x)3 C +C (2 x)2 D +C (2 x)2 CHUYấN TCH PHN Cõu 49: Tỡm e x e x 3dx x (e 3) ex + C B (ex 3) + C 4 A C x (e 3) e x + C Cõu 50: Tỡm sin x cos x + dx 1 (2 cos x + 3)3 + C B (2 cos x + 3)3 + C 3 x x Cõu 51: Tỡm (2 + 3) ln 2dx C (2 cos x + 3)3 + C A A x (2 + 3)4 + C B (2x + 3)4 + C C x (2 + 3)4 + C D 13 x e +C D D cos x + + C x (2 + 3)4 + C Cõu 52: Tỡm nguyờn hm ca hm s f(x) = e2x 1 A f(x)dx = e C f(x)dx = e 2x 1 2x B f(x)dx = e + C +C 2x 2x D f(x)dx = 2e + C +C x2 Cõu 53: Tỡm nguyờn hm ca hm s f(x) = + 2x x3 A f(x)dx = x + + C B f(x)dx = + 2x x + C 3 x3 C f(x)dx = x + + C D f(x)dx = + x x + C Cõu 54: Cho hm s f(x) = Tỡm nguyờn hm F(x) ca hm s f(x), bit F( ) = x A F(x) = 3ln x 2x + B F(x) = ln x 2x + C C F(x) = ln x 2x + D F(x) = ln x 2x + C Cõu 55: Tỡm nguyờn hm ca hm s f(x) = 5x + 3sin 3x A f(x)dx = + cos3x + C B 5 f(x)dx = x cos3x + C C f(x)dx = x + cos3x + C D f(x)dx = x + cos3x + C Cõu 56: Tỡm nguyờn hm ca hm s f(x) = 552x 552x +C A f(x)dx = ln 552x +C B f(x)dx = ln D f(x)dx = 552x + C 2x C f(x)dx = 2.5 ln + C Cõu 57: Tỡm A +C 2x x x dx +2 B ln(x2 + 2) + C Cõu 58: Tỡm nguyờn hm I = A GV cot x ữ+ C B C ln(x + 2) + C dx (sin x cos x)2 cot x + ữ+ C C cot x ữ+ C D +C x +2 D cot x + ữ+ C CHUYấN TCH PHN Cõu 59: Tỡm A B +C x2 C +C x2 D +C (3 x )2 B 3 x x +C C 33 x +C D x x +C B 1 + ln x + C C (1 + ln x)3 + C D (1 + ln x)3 + C x dx + ln x dx 2x (1 + ln x) + C x Cõu 62: Tỡm A dx 13 x +C Cõu 61: Tỡm A 2 +C x2 Cõu 60: Tỡm A 2x (3 x ) x2 + dx B (x + 4) x + + C x2 + + C C x +4 +C D ln( x + 4) + C x Cõu 63: Tỡm ex + 2e dx A 2ex e +C B x Cõu 64: Tỡm (2x + 3)e dx A (2x + 3)e x 2e x + C x + 2ex e +C B (2x + 3)e x e x + C Cõu 65: Tỡm nguyờn hm I = A ln x + + C dx x x x D C (2x + 3)ex + 2ex + C D (2x + 3)ex + ex + C C ln x + x + C D ln x x + C dx B ln x + C x x Cõu 66: Tỡm e (e + 2) dx B (ex + 2)3 + C A ex + + C ex e +C C e1+ 2e + C C x (e + 2)2 + C 2 + e 2x +1 ).4x l: x 2 8 B + e2x +1 + C C + e2x +1 + C x x D x (e + 2)3 + C Cõu 67: Nguyờn hm ca hm s y = f(x) = ( x A + e2x Cõu 68: Tỡm +1 +C 2dx x ln x A ln ln x + C B ln(ln x) + C Cõu 69: Tỡm nguyờn hm I = A 3x + C C ln ln x + C D C 3x + C D ln ln x + C dx x B x + C ex dx Cõu 70: Tỡm x (2e + 3)3 GV x D + 4e2x +1 + C x +C CHUYấN TCH PHN A 4(2e + 3) x +C B 2(2e + 3) x +C C 4(2e + 3) x +C D 2(2e + 3)2 x +C Cõu 71: Nguyờn hm ca hm s y = f(x) = (3 + sin x) cos x l: sin x +C x Cõu 72: Tỡm 2xe dx cos4 x +C A 3sin x B 3sin x + A 2xe x 2e x + C B xex 2ex + C C 3sin x + sin x +C D 3cos x + C 2xe x e x + C sin x +C D 2xex + 2ex + C Cõu 73: Tỡm nguyờn hm I = ex dx A ex + C B ex + C C ex + C Cõu 74: Tỡm nguyờn hm ca hm s f(x) = (3 5x)4 (3 5x)5 +C (3 5x)5 +C C f(x)dx = 25 A f(x)dx = D ex + C (3 5x)5 +C 25 B f(x)dx = D f(x)dx = 20(3 5x) +C Cõu 75: Tỡm x xdx 2 (1 x)2 x (1 x) x + C 2 D (1 x)2 x + (1 x) x + C ln x Cõu 76: Nguyờn hm ca hm s y = f(x) = 2x(x + ) l: x 3 2x 2x 2x 2x ln x + C ln x + C + ln x + C + ln x + C A B C D 3 3 dx Cõu 77: Tỡm x ln x ln x + C A ln x + C B C ln x + C D ln x + C 5x Cõu 78: Tỡm nguyờn hm ca hm s f(x) = x2 1 1 A x + + C B x + + C C 5x5 + + C D x + C x 2x x x x 3x dx Cõu 79: Tỡm x2 x2 3ln x + C A B x + + C C x ln x + C D x2 3x + C 2 x Cõu 80: Tỡm nguyờn hm ca hm s f(x) = cos x.sin 2x x (1 x) x +C 2 C (1 x)2 (1 x) + C A B 1 C f(x)dx = sin 3x + sin x + C 3 1 D f(x)dx = cos3x cos x + C A f(x)dx = cos3x + cos x + C Cõu 81: Tỡm nguyờn hm ca hm s f(x) = GV B f(x)dx = sin 3x sin x + C 3x CHUYấN TCH PHN B f(x)dx = A f(x)dx = 3ln x + C C f(x)dx = ln x + C Cõu 82: Tỡm x x D +C (3 x)2 f(x)dx = ln x + C dx 2 x x +C ln x dx Cõu 83: Tỡm x ln x +C A A B x +C C x +C D x + C C ln x + C B ln2 x + C D Cõu 84: Nguyờn hm ca hm s f(x) = 3x sin 3x l: C x cos3x sin 3x + C ln x +C D x sin 3x + cos3x + C Cõu 85: Tỡm nguyờn hm ca hm s f(x) = cos x x A f(x)dx = tan x + + C B f(x)dx = tan x + + C x x C f(x)dx = cot x + C D f(x)dx = cot x + C x x Cõu 86: Tỡm nguyờn hm ca hm s f(x) = (2x 1) A x cos3x + sin 3x + C B x cos3x sin 3x + C (2x 1)4 +C (2x 1)4 +C D f(x)dx = A f(x)dx = 6(2x 1) + C C f(x)dx = 3(2x 1) B f(x)dx = +C Cõu 87: Cho hm s f(x) = x(1 x)2 Tỡm nguyờn hm F(x) ca hm s f(x), bit F(1) = 2 35 C F(x) = x x + x + 12 x dx Cõu 88: Tỡm x +1 A (x + 1) x + + C x + 2(x + 1) + C C Cõu 89: Tỡm xe x +1dx A F(x) = x x + x A 2xe x +1 + C GV B ex B F(x) = x 2x + x3 + 2 D F(x) = x x3 + x + 12 B (x + 1) x + + x + + C D +1 +C (x + 1) x + x + + C C ex +1 +C D x2 +1 e +C CHUYấN TCH PHN Cõu 90: Tỡm A sin x (2 cos x + 1) +C cos x + dx B +C 2(2 cos x + 1) C +C 4(2 cos x + 1) D +C 2(2 cos x + 1) Cõu 91: Tỡm nguyờn hm ca hm s f(x) = 3x + 3x + + C C f(x)dx = (3x + 2) 3x + + C Cõu 92: Tỡm 2x(2x + 1) dx 3x + + C D f(x)dx = A f(x)dx = B f(x)dx = (3x + 2) 3x + 2) + C (2x + 1)4 + C B (2x + 1)4 + C Cõu 93: Tỡm x(x 3) dx A A (x 3)4 + C B A x3 ln x x3 + C B D (2x + 1)4 + C D x (x 3)4 +C C 2x ln x x + C D x2 ln x x + C ex C ln x ữ+ C e +1 ex D ln x ữ+ C e +1 C (2x + 1)4 + C (x 3)4 + C C (x2 3)4 + C Cõu 94: Tỡm nguyờn hm ca hm s y = f(x) = x ln x x3 ln x + x3 + C Cõu 95: Tỡm nguyờn hm ca hm s f(x) = ex A ln x ữ+ C e 1 e +1 x B ln ( e + 1) + C x Cõu 96: Tỡm nguyờn hm ca hm s f(x) = A tan x cot x + C B tan x + C Cõu 97: Khng nh no sau õy sai? A f (x)dx = f(x) + C sin x.cos2 x C tan x + cot x + C B D cot x + C [f(x) + g(x)]dx = f(x)dx + g(x)dx [f(x) g(x)]dx = f(x)dx + g(x)dx C kf(x)dx = k f(x)dx D Cõu 98: Tỡm nguyờn hm ca hm s y = f(x) = ln x A f(x)dx = x ln x + x + C B f(x)dx = x ln x x + C C f(x)dx = x x ln x + C Cõu 99: Khng nh no sau õy ỳng? A f(x)dx = f (x) + C C f(x) f(x)dx dx = g(x) g(x)dx D B f(x)dx = x ln x + C [f(x) g(x)]dx = f(x)dx g(x)dx D f(x).g(x)dx = f(x)dx. g(x)dx Cõu 100: Tỡm nguyờn hm ca hm s f(x) = x + cos x x3 A f(x)dx = + sin x + C x3 C f(x)dx = + sin x + C GV B f(x)dx = 2x sin x + C D f(x)dx = 10 x3 + cos x + C CHUYấN TCH PHN Cõu 101: Tỡm x(2 + sin x)dx A x + x cos x sin x + C C x x sin x + cos x + C Cõu 102: Tỡm nguyờn hm ca hm s f(x) = A ln x + C B x x cos x + sin x + C D x x cos x sin x + C 2x B ln x + C C ln x + C Cõu 103: Tỡm x(1 x) dx (1 x)4 (1 x)5 (1 x)4 +C + +C B sin x Cõu 104: Tỡm e sin 2xdx A A esin 2x + C C esin x + C Cõu 105: Mt nguyờn hm ca hm s: y = B ln 5sin x A ln ũx D cos x l: 5sin x C ln 5sin x Cõu 106: Tớnh: P = x.e x dx A P = x.e x + C Cõu 107: Tỡm (1 x)5 (1 x)4 +C C B esin x + C A ln 5sin x D B P = e x + C +C (2 x)2 D x (1 x)4 +C sin2 x e +C D ln 5sin x C P = x.e x e x + C D P = x.e x + e x + C dx l: - 3x + 1 - ln +C x- x- B ln x- +C x- C ln x- +C x- D ln( x - 2)( x - 1) + C Cõu 108: Hm s no sau õy l mt nguyờn hm ca hm s f ( x) = x + k vi k 0? x k x + k + ln x + x + k 2 k C f ( x) = ln x + x + k 2 x x + k + ln x + x + k 2 D f ( x) = x +k A f ( x) = B f ( x) = Cõu 109: Nu f ( x) = (ax + bx + c) x -1 l mt nguyờn hm ca hm s g ( x) = A Lc gii: ( 10 x - x + trờn khong x -1 B ổ ỗ ; +Ơ ỗ ỗ ố2 ữ ữ thỡ a+b+c cú giỏ tr l ữ ứ C D 2 Â 5ax + (- 2a + 3b)x - b + c 10x - 7x + (ax + bx + c) 2x - = = 2x - 2x - ) ỡù a = ùù b =- ị a + b + c = ùù ùùợ c = Cõu 110: Xỏc nh a, b, c cho g ( x) = (ax + bx + c ) x - l mt nguyờn hm ca hm s f ( x) = 20 x - 30 x + khong 2x - A.a=4, b=2, c=2 Lc gii: GV ổ3 ỗ ; +Ơ ỗ ỗ ố2 B a=1, b=-2, c=4 ữ ữ ữ ứ C a=-2, b=1, c=4 11 D a=4, b=-2, c=1 CHUYấN TCH PHN ( 2 Â 5ax + (- 6a + 3b)x - 3b + c 20x - 30x + (ax + bx + c) 2x - = = 2x - 2x - ) ùỡù a = ù b =- ùù ùùợ c = Cõu 111: Mt nguyờn hm ca hm s: f ( x) = x sin + x l: A F ( x) = + x cos + x + sin + x B F ( x) = + x cos + x sin + x C F ( x) = + x cos + x + sin + x Lc gii: D F ( x) = + x cos + x sin + x Dựng phng phỏp i bin, t t = + x ta c I = ũ t sin tdt Cõu 112: Trong cỏc hm s sau: t I = ũ ( x sin + x )dx (I) f ( x) = x +1 (III) f ( x) = (II) f ( x) = x +1 + x +1 (IV) f ( x) = x +1 -2 Hm s no cú mt nguyờn hm l hm s F ( x) = ln x + x +1 A Ch (I) B Ch (III) C Ch (II) ổ ữ ữ l hm s no sau õy: ứ xữ Cõu 113: Mt nguyờn hm ca hm s f ( x ) = ỗỗỗ3 x + ố ổ3 ữ x+ ữ B F ( x) = ỗ ỗ ữ ỗ 3ố xứ 12 D F ( x) = x x + ln x + x 5 12 A F ( x) = x x + x + ln x 5 C F ( x ) = ( x x + x ) Lc gii: D Ch (III) v (IV) 2 Â ổ ổ 3 12 ữ ữ ỗ ỗ x x + x + ln x = x + ữ ữ ỗ ữ ỗ ỗ ỗ ố5 ứ ố ứ xữ Cõu 114: Xột cỏc mnh ổ x xử sin - cos ữ (I) F ( x) = x + cos x l mt nguyờn hm ca f ( x ) = ỗ ữ ỗ ữ ỗ ố 2ứ x4 (II) F ( x) = + x l mt nguyờn hm ca f ( x) = x + x (III) F ( x) = tan x l mt nguyờn hm ca f ( x) = -ln cos x Mnh no sai ? A (I) v (II) B Ch (III) Lc gii: (- C Ch (II) D Ch (I) v (III) ln cos x ) Â= tan x (vỡ - ln cos x l mt nguyờn hm ca tanx) Cõu 115: Trong cỏc mnh sau õy mnh no ỳng ? (I) ũ xdx = ln( x + 4) + C x +4 2 A Ch (I) Lc gii: (II) B Ch (III) xdx d(x + 4) = ũ x + ũ x + = ln(x + 4) + C ex Cõu 116: Nguyờn hm ca hm s: y = x l: GV ũ cot xdx = - sin x +C (III) C Ch (I) v (II) ũe 2cos x sin xdx =- 12 ũe 2cos x sin xdx = - e 2cos x + C D Ch (I) v (III) 1 e 2cos x d(cos x) =- e 2cos x + C ũ 2 CHUYấN TCH PHN ex +C B (1 ln 2)2 x ex +C A x ln ex +C C x.2 x e x ln +C D 2x x Cõu 117: Nguyờn hm ca hm s: y = cos l: A ( x + sin x ) + C B (1 + cosx ) + C C x cos + C 2 x sin + C 2 D Cõu 118: Nguyờn hm ca hm s: y = cos2x.sinx l: A cos3 x + C B cos3 x + C B ln(e x + 2) + C Cõu 120: Tớnh: P = sin xdx 3 D cos x + C ex l: ex + C e x ln(e x + 2) + C Cõu 119: Mt nguyờn hm ca hm s: y = A.2 ln(e x + 2) + C sin x + C C 3 B P = sin x + sin x + C A P = 3sin x.cos x + C 3 C P = cos x + cos3 x + C x3 Cõu 121: Mt nguyờn hm ca hm s: y = A x x B ( x2 +4 ) D P = cosx + sin x + C l: x2 C x 2 x 2 x2 D e2 x + C D ( x ) x2 B PHN :TCH PHN Cõu 19: Tớch phõn I = tan xdx bng: A I = D I = C L = D L = C I = B ln2 Cõu 20: Tớch phõn L = x x dx bng: A L = B L = Cõu 21: Tớch phõn K = (2 x 1) ln xdx bng: A K = 3ln + B K = D K = ln C K = 3ln2 2 Cõu 22: Tớch phõn L = x sin xdx bng: A L = B L = C L = D K = 0 Cõu 23: Tớch phõn I = x cos xdx bng: A ln Cõu 24: Tớch phõn I = xe GV x dx bng: A ( ln ) B B C 1 ( + ln ) C ( ln 1) 2 13 D D ( + ln ) CHUYấN TCH PHN ln x dx bng: A ( + ln ) x Cõu 25: Tớch phõn I = Cõu 26: Gi s dx x = ln K Giỏ tr ca K l: B 1 ( ln ) C ( ln 1) D ( + ln ) 2 A B C 81 D 3 x dx thnh Cõu 27: Bin i 1+ 1+ x sau: A f ( t ) = 2t 2t f ( t ) dt , vi t = B f ( t ) = t + t Cõu 28: i bin x = 2sint tớch phõn Cõu 30: Cho I = e2 D f ( t ) = 2t + 2t dx x2 tr thnh: A tdt B Cõu 31: Tớch phõn I = x x b f ( x)dx = v a dx bng: A B dt C dt C D c c a D dt t 0 C I = sin1 D.kt qu khỏc B b cos ( ln x ) dx , ta tớnh c: A I = cos1 B I = x Cõu 32: Gi s C f ( t ) = t t dx bng: A sin x Cõu 29: Tớch phõn I = + x Khi ú f(t) l hm no cỏc hm s C f ( x)dx = v a < b < c thỡ f ( x)dx D bng? A B C -1 D -5 Cõu 33: Tớnh th tớch trũn xoay to nờn quay quanh trc Ox hỡnh phng gii hn bi cỏc ng y = (1 x2), y = 0, x = v x = bng: A 16 B Cõu 34: Cho I = xdx v J = cos xdx Khi ú: A I < J C 46 15 B I > J D C I = J D I > J > Cõu 35: Tớch phõn I = x dx bng: A B C D Cõu 36: Tớch phõn I = x sin xdx bng : A B + C 2 D 2 + Cõu 37: Kt qu ca Cõu 38: Cho dx x l: A f ( x ) dx = Khi ú x x2 1 Cõu 40 Tớch phõn I = x Cõu 41 Tớch phõn I = GV C f ( x ) dx bng:A 2 D Khụng tn ti B C D Cõu 39 Tớch phõn I = B.-1 dx cú giỏ tr l: A 2 B 2 C 2 + 1 3 dx cú giỏ tr l: A ln B ln C ln + 4x + 3 2 x x2 dx cú giỏ tr l:A 2 B 2 C 2 + 14 D ln D 3 D CHUYấN TCH PHN Cõu 42 Cho f ( x ) = x x x + v g ( x ) = x + x 3x Tớch phõn f ( x ) g ( x ) dx bng vi tớch phõn: A (x ) B ( x x x + 2) dx x x + dx 1 C (x ) (x x x + dx + ) x x + dx (x ) x x + dx D tớch phõn khỏc 1 Cõu 43 Tớch phõn sin x cos x dx bng: A ln x+3 C 1 ln 2 D 1 ln 2 x Cõu 44 Cho tớch phõn I = A I > J cos x + 1 + ln 2 B cos x dx , phỏt biu no sau õy ỳng: sin x + 12 dx v J = C J = ln B I = D I = J Cõu 45 Cho tớch phõn I = x (1 + x )dx bng: A (x + x 4)dx x3 x4 B + x3 C ( x + ) D a a 2 Cõu 46 Tớch phõn x a x dx ( a > ) bng:A 8 Cõu 47.Tớch phõn B x 141 142 dx bng: A B 10 10 x C B e2 + e x +1 Cõu 49 Tớch phõn I = x.e dx cú giỏ tr l: A 2 B C a 16 D a D mt kt qu khỏc e + ln x dx cú giỏ tr l:A Cõu 48 Tớch phõn I = x a 16 C e2 + e C D e2 e D e2 e Cõu 50 Tớch phõn I = (1 x ) e x dx cú giỏ tr l:A e + B - e C e - D e 0 Cõu 51 Tớch phõn I = Cõu 52 Tớch Phõn cos x + sin x dx cú giỏ tr l: A ln3 C - ln2 D ln2 sin x.cos xdx bng: A B GV B 15 C D 64 CHUYấN TCH PHN Cõu 53 Nu f ( x )dx =5 v f ( x )dx f ( x )dx = thỡ Cõu 54 Tớch Phõn I = tan xdx l : bng :A B C D -3 A ln2 B ln2 ln2 C D - ln2 Cõu 55 Cho tớch phõn I = x(1 + x )dx bng: A (x ) x2 x3 B + + x dx x3 C ( x + ) D Cõu 56 Tớch Phõn I = ln( x x )dx l : A 3ln3 B 2ln2 C 3ln3-2 D 2-3ln3 Cõu 57 Tớch Phõn I = x.cosx dx l : A + B C 2 + +1 D 2 + Cõu 58 Tớch phõn I = ln[2 + x(x 3)]dx cú giỏ tr l: A ln B 5ln ln C 5ln + ln D ln ln + C.PHN NG DNG TCH PHN Cõu 59 Th tớch ca trũn xoay c gii hn bi cỏc ng y = ( 2x + 1) , x quay quanh trc Oy l: A 50p B 480p C Cõu 60 Din tớch hỡnh phng c gii hn bi cỏc ng A e - ( dvdt ) B e - 1( dvdt ) C 480p A GV p ( 3p - 4) B e - 1( dvdt ) D p l: p ( 5p + 4) C p ( 3p + 4) 48p y = ( e + 1) x , y = ( + ex ) x l: Cõu 61 Th tớch ca trũn xoay c gii hn bi cỏc ng y = y = 0, x = 0, y = D =0 ,y=3 , D 16 p ( 3p + 4) e + 1( dvdt ) x.cos x + sin2 x , CHUYấN TCH PHN y = sin 2x, y = cosx v hai ng Cõu 62 Din tớch hỡnh phng c gii hn bi cỏc ng thng x = , x = A p l : B ( dvdt ) ( dvdt ) C D ( dvdt ) Cõu 63 Din tớch hỡnh phng gii hn bi y = x, y = sin x + x A B 2 ( dvdt ) ( < x < ) cú kt qu l C D Cõu 64 Th tớch trũn xoay gii hn bi y = ln x, y = 0, x = e quay quanh trc ox cú kt qu l: A e B ( e 1) C ( e ) D ( e + 1) Cõu 65 Th tớch trũn xoay gii hn bi y = ln x, y = 0, x = 1, x = quay quanh trc ox cú kt qu l: A ( ln 1) B ( ln + 1) C ( ln + 1) Cõu 66 Din tớch hỡnh phng c gii hn bi cỏc ng A ( dvdt ) B ( dvdt ) D ( ln 1) y = x2 - 2x v y = x l : C - ( dvdt ) 2 D ( dvdt ) Cõu 67 Cho hỡnh phng (H) c gii hn bi ng cong (C ) : y = x3 , trc Ox v ng thng x= Din tớch ca hỡnh phng (H) l : A 65 B 81 64 C 81 64 D.4 Cõu 68 Th tớch vt th quay quanh trc ox gii hn bi y = x , y = 8, x = cú kt qu l: A ( 37 9.25 ) B 9.26 ) ( C ( 37 9.27 ) D ( 37 9.28 ) Cõu 69 Cho hỡnh phng (H) c gii hn bi ng cong (C ) : y = ex , trc Ox, trc Oy v ng thng x = Din tớch ca hỡnh phng (H) l : A e+ B.e2 - e + C e2 +3 D e2 - Cõu 70 Cho hỡnh phng (H) c gii hn bi ng cong (C ) : y = tớch ca trũn xoay cho hỡnh (H) quay quanh trc Ox l : A 3p GV B 4p ln2 C.(3- 4ln2)p D.(4 - 3ln2)p 17 2x + , trc Ox v trc Oy Th x +1 CHUYấN TCH PHN Cõu 71 Cho hỡnh phng (H) c gii hn bi ng cong (C ) : y = ln x , trc Ox v ng thng x = e Din tớch ca hỡnh phng (H) l : B - e A.1 C.e D.2 Cõu 72 Cho hỡnh phng (H) c gii hn ng cong (C ) : y = x3 - 2x2 v trc Ox Din tớch ca hỡnh phng (H) l : A 11 B C 12 D 68 Cõu 73 Din tớch hỡnh phng c gii hn bi hai ng y = x v y = x2 l : A B C D Cõu 74 Hỡnh phng gii hn bi ng cong y = x2 v ng thng y = quay mt vũng quanh trc Ox Th tớch trũn xoay c sinh bng : A 64p B 128p C 256p D 152p Cõu 75 Din tớch hỡnh phng gii hn bi y = sin x; y = cos x; x = 0; x = l: A B C D 2 Cõu 76 Cho hỡnh phng (H) c gii hn bi ng cong (C ) : y = sin x , trc Ox v cỏc ng thng x = 0, x = p Th tớch ca trũn xoay cho hỡnh (H) quay quanh trc Ox l : A.2 B.3 C D Cõu 77 Din tớch hỡnh phng gii hn bi y = x + sin x; y = x ( x ) l: A B Cõu 78 Din tớch hỡnh phng gii hn bi y = A.1 B ln2 C D x3 ;y= x x2 l: C + ln2 D ln2 Cõu 79 Din tớch ca hỡnh phng gii hn bi ( C ) : y = x x ; Ox l: 31 31 32 33 A B C D 3 3 Cõu 80 Gi ( H ) l hỡnh phng gii hn bi cỏc ng: y = x x ; Ox Quay ( H ) xung quanh trc Ox ta c trũn xoay cú th tớch l: 81 83 83 81 A B C D 11 11 10 10 GV 18 CHUYấN TCH PHN Cõu 81 Din tớch ca hỡnh phng gii hn bi ( C ) : y = x + x ; y = x + l: A B C 11 D x Cõu 82 Din tớch ca hỡnh phng gii hn bi ( C ) : y = ; d : y = x + l: C ln D 25 24 Cõu 83 Din tớch ca hỡnh phng gii hn bi ( C ) : y = x ; ( d ) : x + y = l: A ln B A B C 11 D 13 2 Cõu 84 Din tớch ca hỡnh phng gii hn bi ( C ) : y = x ; ( d ) : y = x l: C 3 Cõu 85 Gi ( H ) l hỡnh phng gii hn bi cỏc ng: y = trc Ox ta c trũn xoay cú th tớch l: 7 A B C 6 A B D x 1; Ox ; x = Quay ( H ) xung quanh D Cõu 86 Gi ( H ) l hỡnh phng gii hn bi cỏc ng: y = x ; y = x ; x = Quay ( H ) xung quanh trc Ox ta c trũn xoay cú th tớch l: 8 A B C D 3 Cõu 87 Din tớch hỡnh phng gii hn bi cỏc ng y = 3x + vi x ; Ox ; Oy l: A B C D 44 Cõu 88 Cho hỡnh (H) gii hn bi cỏc ng y = x ; x = ; trc honh Quay hỡnh (H) quanh trc Ox ta c trũn xoay cú th tớch l: A 15 B 14 C D 16 Cõu 89 Din tớch hỡnh phng gii hn bi th hm s y = x 3x v trc honh l: A 27 B C 27 D Cõu 90 Din tớch hp gii hn bi th hm s y = x + v trc honh l: A B C 3108 D 6216 Cõu 91 Din tớch hỡnh phng gii hn bi hai ng y = x3 + 11x v y = x l: Cõu 92 Din tớch hp gii hn bi hai ng y = x v y = x l: 2048 A B C 40 D 105 Cõu 93 Din tớch hp gii hn bi cỏc ng y = x ; y = ; x = l: x 14 A 8ln B + 8ln C 26 D 3 A 52 GV B 14 C D 19 CHUYấN TCH PHN Cõu 94 Cho hỡnh (H) gii hn bi cỏc ng y = x + ; ta c trũn xoay cú th tớch l: A 13 B 125 C 35 y= x ; x = Quay hỡnh (H) quanh trc Ox D 18 Cõu 95 Din tớch hỡnh phng gii hn bi cỏc ng y = mx cos x ; Ox ; x = 0; x = bng Khi ú giỏ tr ca m l: A m = B m = C m = D m = Cõu 96 Cho hỡnh (H) gii hn bi cỏc ng y = x + x , trc honh Quay hỡnh (H) quanh trc Ox ta c trũn xoay cú th tớch l: A 16 15 B C 496 15 D 32 15 x Cõu 97 Din tớch hỡnh phng gii hn bi cỏc ng y = x ; y = ; x = l: B + ln A ln C Cõu 98 Cho hỡnh (H) gii hn bi cỏc ng y = 443 24 D 25 v y = x + Quay hỡnh (H) quanh trc Ox ta c x trũn xoay cú th tớch l: A 15 B ln 2 C 33 ln D Cõu 99 Din tớch ca hỡnh phng gii hn bi: ( C ) : y = x ; ( d ) : y = x 2; Ox l: A 10 B 16 C 122 D 128 Cõu 100 Din tớch ca hỡnh phng gii hn bi: ( C ) : y = ln x; d : y = 1; Ox; Oy l: A e B e + C e D e GV 20