If ∫ √1+sinx f(x) dx = 2/3 (1 + sinx)^3/2 then

Question

If \(\int \sqrt{1 + \sin x}\,f(x)dx = \frac 23 (1 + \sin x)^{3/2}\) then

(A) f(x) is period function 

(B) f(x) is odd function

(C) f(x) is constant function

(D) None of these

Answer 1

Correct option is (A) f(x) is period function 

Given

\(\int \sqrt{1 + \sin x}\,f(x)dx = \frac 23 (1 + \sin x)^{3/2}+c\)

Differentiating on both sides