Question

If ∫sin³xdx = Acos³x + Bcosx + c then A – B = ________ 

(a) (4/3) 

(b) – (4/3) 

(c) (1/3) 

(d) – (1/3)

Answer 1

The correct option (a) (4/3)   

Explanation:

I = ∫sin³xdx = ∫sin²x ∙ sinxdx 

I = ∫(sinx – sinxcos²x)dx 

put cosx = t 

∴ – sinx dx = dt 

∴ I = ∫– dt + t²dt = ∫(t² – 1)dt = (t³/3) – t + c 

I = [(cos³x)/3] – cosx + c 

by comparison, A = (1/3), B = – 1 

hence A – B = (4/3)