Question

please help this is the second time i post this and the first time was wrong so please help me and show all the steps

[10 pts.) 9. Show how to use IBP to get the the power reduction rule... ſ sin sin"(x)dx sin"-'(x) cos(x) n-1 and then use it to help find the volume m="S sin(x)dx n obtained by revolving the region bounded between y=sinºx.y = 0, x = 0 and X=TT around the x-axis.

Answer 1

solution I= = 5 sin? (x) dx Sin"() = sin""(BC). San (0) I = Site). Sin (x) dx и V I = Suvda u Svoz - Sex Sve lote uring this ) I = sor" (2) -asx] -S(n-1) si a cos2 (-1082) de I - - Supply Csix + 0-1)S Sunp240)(252x de Put, Cos²x = |- Sinx Son "la. (a)(e) +(6-195 Summa (x) {1 - Sm 3c} de I =- Sun Mi Eu) (81() +(0-1) (son 2 dk – () Ssumpade I = -SM-l () () (3) + (0-1){ somme de - (94)Z I + (n-1)] = - Senin 7/2) (0(0) + (n+Ssion=2() de = - Sonnt(0) (0) (0) + (14) Ssan"203) de - Sinn?(x). (a() + Issu uring this formula directly integral of giren function. TI mode 7

solution Sfint) di = - Sina).603(0)4. Simpeca) che ㄲ 7 y=sin 3x ,y=0 OSX 27 Find volume about x-axis = ? Volume, V = 77 6-1 =T TE t 6 6 Shyldt = ST. Sin bx dx TS Sinx de Sin sc. Casx - sirve de = 7[{0-0} + 5 5" sure de 57 S Sinux dx 57 [ {- saiz bey me sente de S7 [ {0-0} + 3 4 5 sens de - 6 6 = 57

= 5T 6 [류 S" Sux de •T IST 24 Sin x=1 Sinx de S = 157 [ {Sinx. berx} + 2-1 2 24 2 6 51. dx Shake ST + = 5T - ST . ST 76 STT To 8 [10-0} 57 [ Ž 5. de ST x S 1. de [x]" [TT-0] ST? 76 572 Volume T6 This is the final volume which is STY, is calculated ly given method.