# A calculus problem by Vinay Agarwal

Calculus Level 4

If $$\displaystyle \int_0^{\pi/2} \dfrac{dx}{a^2\cos^2 x + b^2\sin^2 x}=\frac{\pi}{2ab}$$, then find the value of $$\displaystyle \int_0^{\pi/2} \dfrac{dx}{\left(4\cos^2 x + 9\sin^2 x\right)^2}$$.

×