II I PHUONG PHAP TINH TICH PHAN
1 Cdu 3 |lx + é'ldx bdng
fÂ)dx= \fi(pit))(p\t)dt.
1 Cdu 3 |lx + é'ldx bdng
0 ( a ) e ; (c) 2e ; Trd Idị (b). 71
Cdu 4. sinxdx bang
0
(a) 1 ; (b) 2;
Trd Idị (b).
7t
Cdu 5. I cosxdx bang
0 ( a ) 0 ; ( b ) l ; Trd Idị (a). ( b ) i . ( 2 e - l ) ; (d) 3ẹ (c) 3; (c) 2 ; (d)4. (d)3.
71
Cdu 6. tan xdx bang
0 ( a ) l n ( c o s l ) ; (b)ln(sinl); (c) -ln(cos 1) ; (d)ln(sinl). Trd Idị (c). 1 Cdu 7. ln(x)dx bdng (a) 1 ; (b) 2; (c) - 1 ; (d) - 2 Trd Idị (c). Cdu 8. fê^^'dx bdng 0 (a) — ^ ; (b) 2 J, e ^ + e _ , e ^ - e (c) — r - ; (d) 2 j Tra /dj". (a). HOAT DONG 8 HUdfiQ DJN 3^1 T6P SGK
Bai 1. Hudng đn. Six dung cac tfnh chat cua tich phan cau ạ Hudng đn. Dat 1 - x = t.
Ddpsd-^iS^-l).
10</4
Cau b. Hudng đn. Dat x = t.
4
cau c. Hudng đn. Phan tich 1 1 1
x(x + l) X x + 1
Ddp sd. In 2.
cau d. Hudng đn. Phan tich thanh da thiic.
Ddp sd. 11 -5- •
cau ẹ Hudng đn. Ta cd l - 3 x 1 3x
(x + lf (x + 1)' (x + lf Dat X + 1 = t.
Ddp sd. (4 ^
' 3 - 3 1 n 2
cau g. Hudng đn. Ta cd sin3xcos5x = —(sin 8x - sin 2x). Dat 8x = t va 2x = u
Ddp sd. 0.
Bai 2, Hudng đn. Sir dung cac tinh chat cua tich phan.
2 1 2
Cau ạ Hudng đn. [ | l - x | d x = [ | l - x | d x + [ | l - x | d x =
= j ( l - x ) d x + f ( x - l ) d x (adsbygoogle = window.adsbygoogle || []).push({});
Ddp sd. 1.
/^» u ff ' J- T. . • 2 l-cos2x
cau b. Huang dan. Ta co sm x =
Ddp sd. n
cau c. Hudng đn. Ta cd e2x+i+i ê^^' 1 + — . Dat ê = t . e" e"
Ddp sd. e + —.
cau d. Hudng đn. Ta cd sin2x.cos^x = ^ sin2x(l + cos2x)
= — sin2x + — sin4x.
I 4 Ddp sd. 0.
Bai 3. Hudng đn. Sit dung cac tfnh chdt cua tfch phan. cau ạ Hudng đn. Dat u = x + 1.
Dap sọ —.
cau b. Hudng đn. Dat sinx = t.
Dap sọ — ^ 4
Cau c. Hudng đn. Dat u -1 + xê) .
Ddp sd. ln( 1 + e).
cau d. Hudng đn. Dat x = a s i n ^ •
Dap sọ —
6
Bai 4. Hudng đn. Sii dung cac tinh chat cua tfch phan. Phuong phap tfch phan
tirng phan.
cau ạ Hudng đn. Dat u = x + 1, dv = sinxdx.
Ddp sd. 2.
cau b. Hudng đn. Dat u = Inx, dv = x ' dx.
Ddpsd. -i2ê+\).
Cau c. Hudng đn. Dat u = ln(x+l), dv = dx.
1
cau d. Huang đn. Tinh f(x^ -l)e"^dx , M = x" - 1, dv = édx.
0
Ddp sd. - 1.
Bai 5. Hudng đn. Six dung cac tinh chdt ciia tich phan. Phuong phap đi bien sd (adsbygoogle = window.adsbygoogle || []).push({});
va phan tich phan thiic thanh tong cac phan thiic.
cau ạ Hudng đn. Dat u = 3x + 1.
P ^^- 25 x-'-l 3 x-'-l 3 cau b. Hudng đn. Ta cd -^— = x + 2 + -x ^ - l x + 1 ^ . . 1 , 3 Dap sọ — + in — o /
cau c. Hudng đn. Ta cd sin2x.cos\ = - s i n 2 x ( l + cos2x) = - s i n 2 x + -
sin4x.
Ddp sd. 0.
Bai 6. Hudng đn. Sir dung cac tfnh chdt ciia tfch phan. Phuong phap đi bien sd
va phuong phap tich phan tiing phdn.
cau ạ Hudng đn. Dat u = 1 - x.
cau b. Hudng đn. Dat M = x, dv = (1 - x) dx.
Dap sọ —
HOAT DONG 9
B^l TfiP BO SUNG
Bai 1. Chiing minh f Odx = 0.
a b
Bai 2. Chiing minh J cdx = c(6 - a).
a b
Bai 3. Chiing minh \kfix) dx = k f/"(x) dx,.
a b
Bai 4. Chiing minh f[/'(x) ± g(x)]dx = f/"(x) dx ± f g(x) dx.
a b
a a c b c b
Bai 5. Chiing minh f/•(x)dx = f/•(x)dx + f/•(x)dx.
a Cl
Bai 6. Chiing minh Neu fix) >0,xe[a; b], thi f/"(x) > 0.
Bai 7. Chiing minh Ifix) dx l\f(x)\ dx.
Bai 8. Neu m < /"(x) < M, x G [a ; 6], m, M la cac hang sd thi
b
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