Question

If ∫(sin3θ + sinθ)cosθe^sinθdθ = (Asin³θ + Bcos²θ + Csinθ + Dcosθ + E)e^sinθ + F, then

(A) A = - 4

(B) B = –12

(C) C = 20

(D) D = 0 

Answer 1

Answer is  (A), (B)

Putting sinq = t, we get

It follows immediately that D = 0.

Differentiating both sides w.r.t. t, we get

(4t − 4t³)e^t = [At³ + (3A – B)t² + (C − 2B)t + C + B + E ]e^t

And hence, A = – 4, B = – 12, C = – 20.