If _ 0 ^ x^ 2 (1+ x)^ 2 d x=A then _ 0 ^ 2 x^ 2 ^ 2 (x / 2) (1+ x)^ 2 d x=
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(\int_{0}^{\pi} \frac{x^{2}}{(1+\sin x)^{2}} d x=A\) then \(\int_{0}^{\pi} \frac{2 x^{2} \cos ^{2}(x / 2)}{(1+\sin x)^{2}} d x=\)
- \(\mathrm{A}+\pi-\pi^{2}\)
- \(\mathrm{A}-\pi+\pi^{2}\)
- \(\mathrm{A}-\pi-\pi^{2}\)
- \(\mathrm{A}+2 \pi-\pi^{2}\)
Answer
(D) A +2 - ^ 2
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