Show that _ 0 ^ /2 dx a^2 ^2 x + b^2 ^2 x = 2ab ; a

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Show that

\int_{0}^{\pi/2} \frac{dx}{a^2 \cos^2 x + b^2 \sin^2 x} = \frac{\pi}{2ab}; \quad a, b > 0.