Questions with Answer for Assignment - Calculus II | MATH 166, Assignments of Calculus

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2 1-cos6t 7 ( 1+ cos6t 1 11. [sint stcos* 3rat = | — ER | at = — [1-207 6+ cos! 6rbat 2 16 1 1 2 1 1 2 =—J)1-+cos1 24) +—(+e0s121)? Jat --— | cosl2tat+— | (1+200812r + eos" 12A)at 16 4 16 64 1 1 1 1 =-—— [12 cosl2tat + — fat+— [12c0s12¢dt+—[(1+cos24ndt 192 64 384 128 sin 24t+C = sint2¢+ t+ sin 244 ts sin 24t+C =r sin tate 1 192 64 384 128 3072 128 384 3072 1400820} (1-c0s 26 1 12. [cos® asin? ade = pseey (HS Jae = jg] U+ 2e0s28-2 cos? 29 - cos! 2a) aa == 49+ | 2e0s20d0-* [a sin ? 28) 082848 [1+ 00840)" de “i “is dé+~ [2e0s28d8—— | 2c0s28d0 += [2sin® 200052040 [(1+ 2e05 48+ cos? 40)de =— 15] 8+ fsin? 20-2605 28 dd - 1 [dé -—— | 4c0s40d0 -—— | (1+ cosse)dé 16 16 64 128 128 = to. 4 gin? 29-46 sinag +9 -1 -cinso ic 16 48 64 128 128 1024 = a+ in} 29-1 singa-—1_ sins +€ 128 48 128 1024 A J xcos” xsinxdx u=x du=ldx dv = cos” xsinx dx : 1 v —| (osx)? (-sin x) de = -— cos? x tecos.x 3 Thus J xcos” xsin xdx = x(- 008? x)- Jar eos* x)dx= 1 x c053 3 vax l= x cos x+ [cos xdx|= -xeos? x+ [eosx(1-sin” sax] = wile fesinx wile th cos? x+ f(cosx —cosxsin” x) a = . 1. =xeo08° x+sinx——sin’? x/+C