A calculus problem by Sabhrant .

Calculus Level 5

π2π2(sinx)200dx\large \displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin{x})^{200} \, dx

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


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