A calculus problem by Pratik Shastri

Calculus Level 4

0π/2sin100xdx0π/2sin102xdx \large \dfrac{\displaystyle\int_{0}^{\pi/2} \sin^{100} x \, dx}{\displaystyle\int_{0}^{\pi/2} \sin^{102} x \, dx}

If the integral above can be expressed as ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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