If , then the value for is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

If ∫0π(x1+sin⁡x)2dx=A\int_0^\pi \left(\frac{x}{1+\sin x}\right)^2 dx = A , then the value for ∫0π2x2⋅cos⁡2x/2(1+sin⁡x)2dx\int_0^\pi \frac{2x^2 \cdot \cos^2 x/2}{(1+\sin x)^2} dx is equal to (1) A+2π−π2A + 2\pi - \pi^2 (2) A−2π+π2A - 2\pi + \pi^2 (3) 2π−A−π22\pi - A - \pi^2 (4) None of these

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