Question

If f(x) = ∫tsintdt for t ∈ [0, x], then f'(x) =

(A) cosx + xsinx

(B) xsinx

(C) xcosx

(D) None of these 

Answer 1

Answer is (B) xsinx

Since f(x) = ∫tsintdt for t ∈ [0, x], Now, according to Leibnitz’s rule,

f'(x) = xsinx.(1) - 0 = xsinx