A calculus problem by Sabhrant .

Calculus Level 5

$\large \displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin{x})^{200} \, dx$

The closed form of the integral above can be expressed as $\dfrac{\pi b!}{a^b (c!)^2}$, where $a,b$ and $c$ are natural numbers. Find $a+b+c$.

Inspiration

×