Tài liệu Làm chủ môn toán trong 30 ngày đại số & giải tích 12 quyển 2 (tt)

S minh hoa vi~c lua chon mot trong hai huong tren, ta co vi du: 1/2 f f(x)dx, vi~c hra chon An phu x = sint,- a. Voi I= 0 1t ~ t ~ 2 1t cho phep ta hra chon huong 1, 2 boi khi do: + Voi x = 0, suy rat= 0. '. 1 7t + V O'l x = - suy ra t = - . 2' 6 1/3 J f(x)dx, b. V6i I= vi~c lua chon An phu x = sint, - 1t ~ 2 0 t ~~ta thuong lua chon huong 2, boi 2 khi d6: + Voi x = 0, suy rat= 0. + V &i x = i, ta khong chi ra dtroc s6 do g6c t. 2. Phuong phap tich phan tirng phin CO' so cua phucmg phap tich phan tung phfu1 lA cong tlnrc sau: J u(x).v'(x).dx b b = u(x).v(x)I. J v(x).u'(x).dx. b - ( 1) b B~ sit dung ( l) trong vi~c tinh tich phan I= J f (x)dx ta thuc hien cac bircc: a Buac 1: Bien d6i rich phan ban d~u v€ dang: b b = I= Jt(x)dx a Jf1(x).f2(x)dx. • Bu&c 2: E>~t: u = f1 (x) { dv = fi{x)dx => {du v · Bu&c 3: Khi d6: I = UV I b b a - f vdu . • Chu y: Khi SU' dung phuong phap tich phan rung phan dS tinh tich phan chung ta c§n tuan thu cac nguyen tic sau: 1. Lua chon phep d~t dv sao cho v diroc xac djnh m{>t each da dang. b f 2. Tich phan vdu duoc xac dinh m9t each d~ dang hem so voi I. a 3. Chung ta c!n nhc cac dang CCY ban sau: Dang 1: Tich phan I= Jxci.lnxdx, voi aeR\{-1} khi do d~t u = lnx. Dang 2: Tich phan 1 = JP(x)ecixdx (hoac I= JP(x)eQJCdx) v&i P la m9t da thirc thuoc R[X) va aeR" khi c16 d~t u = P(x). Trai nghiim Ht sinh thai Hoc Website: maloda.vn di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang 123~ Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Chuang Ill - Nguyen ham, tlch phiin wi trng dung Dang 3: Tich phan I= JP(x)sina.xdx (hojic JP(x)cosa.xdx) voi P la mc}t da thirc thuoc R[X] va a.eR" khi d6 d~t u = P(x). Dang 4: Tich phan I = feaxcosbxdx (hoac feaxsin(bx)dx vci a, b f. 0 khi d6 d~t u = cos(bx) (ho~c u = sin(bx)). B. PHAN LO,.;.I v A PHUONG PHAP GIA.I cAc D,.;.NG TOAN Phuong phap d8i bil11 d{lng 1 Phuong phap Sfr dung ki€n thirc trong phuong phap 1 cua phin phuong phap d6i bi~n s6. Vi d1.1 l: Tinh tich phan: I rt/3 I= 11/6 d cosx. x . sin 2 x - 5 sin x + 6 f>~t t = sinx, suy ra dt = cosx.dx f>6i c~: 1t l 6 2 7t .fj •x=-=>t=-. •x=-=>t=-. 3 2 Taco: cosxdx dt sin? x-5sinx + 6 t2 -5t+ 6 ------= dt =---(t-2)(t-3) = (~ ~)dt= + t-3 , d,o: tu {A+ B=0 -2A-3B=l Suy ra: ~ t-2 [(A+B)t-2A-3B]dt (t-2)(t-3) {AB=-1 =l . (-1- __ l_) cos xdx = sin 2 x - 5 sin x + 6 t- 3 t- dt. 2 Khid6: I= J"r(-1- 112 Lrrang t-3 124 Website: maloda.vn _l_)dt = t-2 lnl t-311.[J,2 t-2 1/2 = ln 3(6-.fi). 5(4-.fi) Trai nghi/m Hi sinh thai H()c di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Sung Cac em hQC sinh hay: l(lO: + Tao ra m<)t bai toan nrong nr. + Tao ra cau hoi trllc nghiem tu n9i dung vi du tren. C/111 j: Ti~p theo, chung ta xet vi du voi viec hra chon • Vi di} 2: Tinh tlch phan I = D~t t = 1 + sin2x, J cos x.si_n rt/2 • 3 0 1 +sm x 2 x. dx An phu t bing ca m§u s6. . suy ra dt = 2sinx.cosx.dx. Df>i c~: • x=O=>t= 1. 7t • x= - => t=2. 2 Tac6: cosx.sin3 xdx = sin2x.cosx.sinxdx l+sin2x I+ sin 2 x = (t-l)dt 2t = _!_(t -!)dt. 2 t Khi d6: 1 2 I= - 2 1 f Cl--)dt t 1 1 =-(t-lnltl)I 2 1 2 2 = -(l-ln2). 1 Sang too: Cac em hQC sinh hay: + Tao ra mot bai toan nrong tu. + Tao •vidi} 3: ra cau hoi trllc nghiern tu n(>i dung vi du tren. dx J 2sinsmx2+x.cos' . x rt/6 Tinh tich phan I= 0 • 2 D~t t = 2sin2x + cos-x, suy ra dt = sin2xdx J:'\,t. " uo1 can: • x=O=>t=l. 7t 5 .x=-=>t=-. 6 4 Khid6: 514 I= dt J-t = In It 1 S/4 1 5 = In4. l Sang tqo: Cac em hQC sinh hay: + Tao ra m<)t bai toan nrong tu, + Tao ra cau hoi trllc nghiem tu n<)i dung vi du tren. Trai nghiim Ht sinh thai Hoc Website: maloda.vn di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang 125~ Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Chuang Ill - Nguyen ham, tlch phiin Vi du 4: Tinh tich phan I = '}2 ~ ex +2 O r.--= ..2 ...Jex + 2 => r ¥ f)~t t = . 2tdt ex + 2, suy ra: 2tdt = e'dx ~ dx = -2t -2 = D6ic~: • x=O=>t=JJ. • x = ln2 => t = 2. Khid6: wi trng dung • ~~r = _1_ ln = _1_ In (2-J2)( Jj + J2) 2J2 ~.,13 2J2 (2+J2)(fi-J2)' I= J2~ .J3t2-2 Sang tpo: Cac em hQC sinh hay: + Tao ra mQt bai toan tucmg nr. + Tao ra cau h6i tr&c nghiem tu n9i dung vi du tren . .J3 Vi di} 5: Tinh tich phan I= J x .J1 + x dx. 5 2 0 D~t t = .J1 + x2 , suy ra: t2 = 1 + x2 => 2tdt = 2xdx D6i c~n: • x=O=>t= • x = fi Khi d6: 1. => t = 2. 2 2 I= J(t2-t)2t2dt= t Sang ( J(t6-2t4+t2)dt= f(J.O: 1 25+-t31 ) 2 =-. 848 -t7--t 7 t 5 3 1 105 Cac em hoc sinh hay: + Tao ra m9t bai toan tuong tu, + Tao ra cau hoi tr&c nghiem tu nQi dung vi du tren. 11/2 Vi du 6: Tinh tich phan I= J .Jcosx.sin 3 x.dx. 0 D~t t = .Jcosx thl t2 = cosx suy ra 2t.dt = +sinx.dx. D6ic~: • x=O=>t=l. • x =- 1t 2 => t = 0. Lrrang126 Website: maloda.vn Trat nghiem Ht sinh thai H9cdi 6. 0- SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Ta co: .Jcos x sirr'x.dx = sin'x .Jcos x .sinx.dx = = (1 - cos'x) .Jcos x sinx.dx (1 - t4).t.< - 2tdt) = 2(t6 - r)dt. J Kb 1. db : I = 2 0(t 6 - t2 )dt = 2( -1 t7 - -1 .3 r) Io = -s . 1 7 3 I 21 Sang tao: Cac em hQC sinh hay: + Tao ra met bai toan tuong tu. + Tao ra cfiu hoi tr&c nghiem tu n<)i dung vi d1,1 tren. Ji J ~x +I . • Vi dy 7: Tinh tich phan I= JJX D~t t = ,2 r = 2 ..f x2 + 1 suy ra: 2 x + 1 => t.dt = x.dx ~ dx t.dt = - x => tdt d:x dt = -2- = -2x t t -1 x~ • D6i cin: = .J3 => t = 2. x = ./8 => t = 3. • x • Khi d6: I= J .z., = .!. lnl t- l 1 -1 2 t2 2 t +1 3 2 = .!.1n I. 2 2 Sang tao: Cac em hQC sinh hay: + Tao ra m(:>t bai toan nrong nr, + Tao ra cau hoi tric nghiem tu n9i dung vi d1,1 tren . Vi di} 8: Tinh tich phan I = f ~3d . .fi 3 o Datt= · t3 = x2 + 1 => 3t2dt = 2xdx <:::> dx = 3t2dt 2x . r.~· can: " :uo1 .x=O=:>t=l. • x= Ta c6: Ji => t = 2. x'dx x3 .3t2dt = 0 a. Vi xe(O; 2) nen: { . x+2>0 fl~t t = J;:+I. + dt = ( .Jx + 2 suy ra: 1 + 1 ) dx = ( ,J;+i + ~ )dx <=> dx 2J;:+i 2.Jx + 2 2.j(x + l)ex + 2) .Jex+ l)ex + 2) 2dt t fl6i c~n: • x=l=>t=l+.J2. • x=2=>t=2+./3. Khi d6: 2 I= ! dx 2+Jj dt 2+Jj .Jex+ l)(x + 2) = 2 ,.~-1 = 2lnlt"'+.Ji b. Vi xe( -5; -3) nen: 2 + J3 = 2ln l + J2 . x + 1 <0 . { x+2<0 D~t t = .J-ex + l) + .j-(x + 2) suy ra: d -[ 1 l t- 2.j-(x + 1) 2.j-(x + 2) <=> .:.. £) 01 dx 2dt =-.j(x + l)(x + 2) t Jd _ x- - [.j-ex+l)+.j-(x+2)]dx 2.j(x + t)ex + 2) · " can: • x=-5=>t=2+./3. • x=-3:=>t=l+.J2. Khi do: -3 dx I = L-.J;=(x=+=l=)e=x=+=2==-)= - 2 L Trang 128 Website: maloda.vn it t 1+./1 dt I 2 + fj = 2lnltl i+../2 = 2ln 1 + J2 2+Jj . Trat nghiem Ht sinh thai H9cdi 6. 0- SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ miin TOAN trong 30 ngay - Giai tlch I 2 - Quydn 2 b C/u, y: Nhir vay, d~ tinh tich phan: I= f '1(x + a)(x dx , + f3) a ta dn xet xem trong (a, b) dAu cua cac x + a. va x + f3 la fun hay dirong. DiSu nay chung ta phan tlch ky trong ph!n ti ch phan ham s6 ti bei c6 th~ sir dung bi~n d6i Euler: vo '1(x + l)(x +2) = t(x + se 1). Sang tao: Cac em hQC sinh hay: + Tao ra mQt bai toan nrong tu, + Tao ra cau hoi tric nghicm nr nQi dung vi d1,1 tren. • Vi di} 10: Tinh tich phan: I= 2r . tt/2 2dx 2smx-cosx+l . x 1 Datt= tan-2, ta duce: dt = -2. 1 2 x 1 2 2dt dx =- .(1 + tan - )dx =- .(1 + t )dx <=> dx = --2 • v cos" ~ 2 2 1 +t 2 2 D6i c~: ·x=~=>t=l. 2 27t • x= => t = fj . 3 Khid6: 4dt I= JjJJ 1 + t2 - JjJ3 2dt -2 JjJ3 d(t + 1) - In I _i!__ l-t2 +l I l2 +2t I (t+l)2 -: 1 + t2 1 + t2 1_!_]"3 = In 1+2)1 3-J?, fj +2. Sang tao: Cac em hQC sinh hay: + Tao ra mQt bai toan tucmg tu, + Tao ra cau hoi tric nghiern tu noi dung vi d1,1 tren. Chu y: Ti~p theo, chung ta se xet mot vii vi d1,1 voi viec hra chon in phu dua tren cac tinh ch~t cua ham s6 duoi d!u tich phan. tt/2 Vi di} 11: Tinh tich phan I= J cosx dx. o -./8-2sin2 x D~t t = sinx thi dt = cosxdx. " can: • x = 0 => t= 0. .l.· f)01 rt •X=-=>t=l. 2 Trai nghiim Ht sinh thai Hoc Website: maloda.vn di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang/29~ Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Chuang Ill - Nguyen ham, tlch phiin Khi do: I = ft · dt = _1_J1 dt Ji o '14-t2 o Js-2t2 wi trng dung • DJt t = 2sinu thl dt = 2cosudu. D<3i can: • t = 0 => u = 0. 1t • t=l=:>u=-. Khi d6: I= 6 -·ho-T = 2cosudu J4-4sin2u _l_T J2 du = -•-ur/6 = ~- J2 ° 0 6h NJ,~,, xet: Nhir v~y, n~u chung ta da c6 duce chut kinh nghiem thi co th~ chi phep d<3i bien, cu th~: = 2sinu D~t sinx l• f) 01 can: thi cosxdx d.n thuc hien IDQt = 2cosudu. A 0 => u = 0. • X = 1t • x=- 2 Khi do: I= =:>u=-. f 2 tt/2 1t 6 f d 1 cosu u -- o '18-8sin2 u n/6 d l cosu u =- hoJI-sin2u 1 f du =-ul~'6 11./6 lio Ji = ~- 6Ji Sang tao: Cac em hQC sinh hay: + Tao ra m¢t bai toan nrong nr. + Tao ra cau hoi tr&c nghiem tu n9i dung vi du tren. Vi dy 12: Tinh tich phan I = I 4 Ox x~ . +x +l f)~t t = x2 thi dt = 2xdx. l· ,.. f) 01 can: • x = 0 => t= 0. • x=l=:>t=l. . d'. I--- 1 JI dt Kh IO . 2 0 t2 +t+l _ l Datt+ · 2 _ 1 Jl dt 2 0 (t+.!.)2 2 -- J3 , = -tanu thi: 2 J3 +l. du 4 .fj 2. dt= -.-= -(1 + tan-u)du. 2 cos2 u 2 D6ic~: • t=O=:>u= • t=l::>u=-. L Trang 130 Website: maloda.vn 1t -. 6 1t 3 Trat nghiem Ht sinh thai H9c di 6. 0- SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Khi d6: .fj 2 + tan u)du 1 "'3 -(1 I=2 J 2 I tan 1116 u+ 2 4 I "'3 1 J du =-ul .fj 1 =- .fj nt6 ,.,3 1t =-. 6J3 1('6 4 Sang t(JO: Cac em hoc sinh hay: + Tao ra m(:>t bai toan nrong tu, + Tao ra cau h6i tric nghiem tu nQi dung vi d1,1 trcn. = Vi d\l 13: Tinh tich phan I J .J9 + 3 x dx . 2 1 2 X D~t x .fj = 3tant thl x = .fj tant, t e(D6i c~: • x=l~t=-. 1t , 2 2:.) suy ra dx = 2 ~ cos dt. t 1t 6 •x=.fj~t=2:.. 4 Khi d6: + 9tan x I ~9tan x - .fj 2 n/4 I- 2 - "'14 . -2- t COS "'6 I dt - ttl6 "I'4 .fidt COS . t.sm 2 l = ,,,,6 fj cos t.dt (1-sin2 t).sin2 t · D~t v = cost, suy ra dv = - sintdt A· ,.. D OlC~: 1t 1 6 2 1t Ji 4 2 .t=-~v=-. •t=-~v=-. Khi d6: f t: lt/4 I= 1116 v3cost.dt . 2 t ) .sm. 2 t (1 - sm J (1v = .fj ./212 112 1) -2--2- v -1 = t: Ji 12 f 112 (1 v3dv - dv = .fj v 2) . v 2 = .Ji /2 f .fie-) __ 1 _)dv 1 "2 v2 ( ----1n J t 1v-ll)Ji v 2 v+l 12 v2 - = .fj[2- 112 1 .fi.+2 J2 + -ln-----=-J. 2 3(2-.fi.) Sang lflO: Cac em hQC sinh hay: + Tao ra m(:>t bai toan tuong + Tao ra cau h6i tric nghiem Trai nghiim Ht sinh thai Hoc Website: maloda.vn tu, tu n(:>i dung vi d1,1 tren. di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang 131.~ Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Chuang Ill - Nguyen ham, tlch phiin wi trng dung Phuong phap i/Ji biJn dtJng 2 Phuong phap Su dung lci~n tlnrc trong phtrong phap 2 cua phful phuong phap d6i bi~n s6. 112 Vi du l: Tinh tich phan I= J .J1-x dx. 2 0 Ta c6 th~ trlnh bay theo cac each sau: Cach 1: f)~t x = sint, - 2:. 5t5 2 2:. suy ra dx = cost.dt 2 nA· " .uo1 can: +V6ix=Othit=O ,. l hl1t=-.1t + Vmx=-t 2 6 Khid6: ~6 ~ J .J1-sin t.cost.dt I= = 2 0 J cos t.dt 2 0 1 + = -(t 2 1 . I "''6 -sin2t) 2 1~ =(l+cos2t).dt 2 0 J 1 1t + -). J3 = -(2 6 0 4 Cacb 2: f>~t x = cost, te [O; 1t] suy ra dx = -sint.dt. A· f)01 " can: + V oi x = 0 thi t = n . 2 '. l h'1t=-. 7t + Vmx=-t 2 3 Khi d6: rt/3 J J1-cos t.sint.dt I=- 2 11/3 J sini t.dt =- 11/2 rt/2 } 1 2 2 . =--(t- -sm2t)I x/3 n/2 1 7t l x/3 2 r,/2 =-- J (1-cos2t)dt J3 = -(- + -). 2 6 4 Sa11g l(JO: Cac em hQC sinh hay: + Tao ra m<)t bai toan tuong tu. + Tao ra cau hoi tric nghiem nr n{>i dung vi du tren. Lrrang 132 Website: maloda.vn Trat nghiem Ht sinh thai H9cdi 6. 0- SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Lam chu miin TOAN trong 30 ngay - Giai tlch I 2 - Quydn 2 2 Vi du 2: Tinh tich phan I= I x ..f 4- x dx. 2 2 I D~t x = 2sint, - 5: t 5: 1t 2 1t 2 suy ra dx = 2costdt D6i c~n: + V&i x = 1 thi t= 1t 6 + V6i x = 2 thl l = 2:. 2 rr.12 rr.12 J 4sin t...f4-4sin t.2cost.dt=4 Khid6:I= 2 J sin' Zt.dt 2 1'.16 ,ell =2 rr.16 l . ) =2 ( t--sm4t «n 4 ../3) . =2 ( -1t + 3 1116 J (l-cos4t).dt 11(6 8 Sa11g t90: Cac em hQC sinh hay: + Tao ra mot bai toan nrong nr. + Tao ra cau b6i tric nghiem tu noi dung vi du tren. Vi dy 3: Tinh tich phan I= 'Yo ~1-x . Ta c6 thB trlnh bay theo cac each sau: Cach 1: D~t x = sint, _,?: < t < 2: suy ra dx = cost.dt. 2 2 D6i c~n: • x = 0 => t= 0. 1 1t • x=-=:>t=-. 2 6 Khi do: I= f .J1cos- sint.dt t = f coscostt.dt = f dt = tl:'6 rr./6 2 0 tt./6 rr./6 O O = 1t6. Cdch 2: D~t x = cost, te(O; 1t) suy ra dx = -sint.dt. f)f>i can: + vui x = o thi t= 2 .l..' + Vvl X = -1 thi1 t = 2 Khi do: I =-T «n Sang 1t . -1t . 3 sin t.dt = -Tsin t.dt _ «n sin t .Ji - cos' t -T rr.11 dt =- tl•'3 "'2 =- ( 1t _ 1t) 3 2 = 1t. 6 Cac em hQC sinh hay: + Tao ra m{>t bai toan nrong tu, + Tao ra cau h6i tric nghiern tu n9i dung vi du tren. t(JO: Trai nghiim Ht sinh thai Hoc Website: maloda.vn di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang133~ Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ Chuang Ill - Nguyen ham, tlch phiin • J• ~(l-x2)3 dx b Vi dy 4: Tinh tich phan I = J3 . a. V 6i a = 0 va b = nu~t a. wi trng dung b. Voi a= Ova b 2 = .!. . 3 · x = smt, - -1t < t < -1t suy ra dx = cost. dt. 2 2 ... " f) OIC~: + V6i x = 0 thl t = 0. + VO'l,. x = J3 - hi t = -1t . t 2 3 Khid6: Iin J 1 -_ dx ---;::::=== I o \I (1- J 1113 = 2 3 I d cost. t o V (1- X ) · Slll 2 d J cost. d = J--t= tantl"'J o 11/3 = t) 3 n/3 t 0 COS 3t O COS 2t = J3. b. Ta lira chon huong xac dinh nguyen ham: [ J \I'(t-xdx ] =f cos t.dt =f ~ = tant+c= sin t cos3t cosi t cost 2)3 + c. x J1-x2 X•Slnl 113 Khi d6: I= +c- 1 x J1-x2 0 - 2-fi. · Ch11 j: 1. Trong loi giai cua cau b) sa d1 ta c6 ~(l-x )3 = cos3t va tant = 2 la boi: x .J1- x 2 -- 1t {.Jcos 1t 2 < t < - ~ cost> 0 ~ 2 t = cos t . cost=Jl-sin2t=Jl-x2 2 Tuy nhien, chung ta hoan toan c6 th~ thirc hien theo huong l, thijt vay: -! IIJ 1- [ 2. cAn d~ 11 dx ] ~(l-x2)3 xcainl - ...!. 0<:1 <:11 , vo, sin 11 y r~ng, dung ! dt - tant II cos2 t 1° 3 huong 2 th1 khi d6i bi€n s8 ck don anh t H x = q>(t) dS d6i k€t qua tu t sang x, con voi huong 1 thi khong cftn. Sang tao: Cao em bQC sinh hay: + Tao ra mQt bai toan nrong nr. + Tao ra cau L Trang 134 Website: maloda.vn hoi tric nghiem tu nQi dung vi d1,1 tren. Trat nghiem Ht sinh thai H9cdi 6. 0- SPBook Facebook: www.facebook.com/Maloda.vn Hotline: 0972.853.304 MALODA.VN - KHO SÁCH QUÝ, THI HẾT BÍ f 4/./i~dx .. Vi dy 5: Tinh rich phan I= x x 2 2 sin2t' Dat x = -· 0~t~ E>6i c~n: • x=2=>t=~. 1t suy ra dx = - 4 • 3 • 4cos2t.dt . sin22t - 4 4 7t Jj 6 •x=-=>t=Khid6: I =_ 4cos2t.dt J "'6 • 2 sin 2t 11/4 -- _ 8 sin" 2t 1 ,r/6 2cot 2t. ,r/4 -- J J cosi Zt.dt =-- J (l+cos4t).dt 11/6 =- 2 rr./4 4cos2t.dt 2 sin 2t 8 sirr' 2t 1 11/6 1 . 2 rr./4 4 1t ,r/6 =--(t+ -sm4t)I =x/4 24 Jj - -. 16 Sang tqo: Cac em hQC sinh hay: + Tao ra m{>t bai toan tuong tu, + Tao ra cau hoi tric nghiem tu n{>i dung vi du tren. Vi d~ 6: Tinh tich phan I = 21./i dx J ~ . 2 XX-) _ 1 E>~t x = -.- sin t n te(O; - ) suy ra dx = , 2 - cost -.-dt. sini t E>f>i can: 1t • x=l=>t=-. 2 2 7t Jj 3 •X=-=>t=-. Khid6: 1 tdt 1112 --.-2-cos I= J sm t rr./3_1_~ sin t =- 1 -1 sin2 t Trai nghiim Ht sinh thai Hoc Website: maloda.vn ,r/2 J dt =-tn/3l rr./2 7t =-6. 11/3 di 6.0-SPBook Facebook: www.facebook.com/Maloda.vn Trang 135~ Hotline: 0972.853.304