Prove that _ 0 ^ /2 dx (a^2 ^2 x + b^2 ^2 x)^2 = (a^2 + b^2) 4a^3 b^3

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Prove that ∫0π/2dx(a2sin⁡2x+b2cos⁡2x)2=π(a2+b2)4a3b3\int_{0}^{\pi/2} \frac{dx}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} = \frac{\pi(a^2 + b^2)}{4a^3 b^3}

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