Question

i think the answer is pi but im not sure please show all steps

Evaluate the following integral using integration by parts. Show all work including equations for u, du, v, and du ſ esinada

Answer 1

So x sin(x) dx integration by parts detination: Suvia uv-Su'v К. v'= sin(x) ul. d v=) sin(as de (X) dx - -cos (x) =) TO Juul (9.6-c0s (8)) - 1.6-6056) Dr) u ñ 22. Cos (x) 2) - SC-605(2)) an] cos(x) dx ET =) - S Cos (0) dx Common integral cu 2 use the BE =) - Sin (x) " Cos(a) - (sincs) (- X. o T 11 {-x.cos(x) + Sincas]

Compute the boundries! fca) S f(a)dx=lim f (x) - lim 2-7b- 3-at a bat f(x)= (-3651x)+sin(x)) => lim 2-)ot (-x65 () + sin(x)) ou ui bola Value x=0 (= -o coscoot sin (0) >) -0.1 to Cosco)-1 sin coco => 0 > lim x-is- (-x.cos( w) tsiness) Value x=7 plug in the -) -T.COS (1) + sin (IT) cos(a)= -1 = –ū(-1) to sin (IT) =0 =? T = T - TT. Thank you so much