The value of ∫ x^2 cos x / 1 + e^x ; x ∈ (-π/2 , π/2) dx is equal to

Question

The value of \(\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\) \(\frac{x^2cosx}{1+e^x}\) dx is equal to

(A) \(\frac{\pi^2}{4}-2\)

(B) \(\frac{\pi^2}{4}+2\)

(C) \(\pi^2-e^{\frac{\pi}{2}}\)

(D) \(\pi^2 +e^{\frac{\pi}{2}}\)

Answer 1

Correct option is (A) \(\frac{\pi^2}{4}-2\)