Interesting Integrals 10
Calculus
Level
4
\[\large\int_{0}^{\sin^2 (x)}{\sin^{-1} \left( \sqrt t \right)}\,dt\ + \large\int_{0}^{\cos^2 (x)}{\cos^{-1} \left( \sqrt t \right)}\,dt=\dfrac{\pi}{c} \]
The equation above holds true for some positive integer \(c\). Find \(c\).
by
Krishna Shankar