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Question

Question: Find value of \( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+\sin x \cos x} d x\)...

Find value of ∫0π2sin⁡2x1+sin⁡xcos⁡xdx \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+\sin x \cos x} d x

A

π4\frac{\pi}{4}

B

π2\frac{\pi}{2}

Answer

π2\frac{\pi}{2}

Explanation

Solution

To solve the integral, we can use the substitution method and properties of definite integrals. By transforming the integral and utilizing symmetry, we find that the value of the integral is π2\frac{\pi}{2}.