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∫0π/2sin100x dx∫0π/2sin102x dx \large \dfrac{\displaystyle\int_{0}^{\pi/2} \sin^{100} x \, dx}{\displaystyle\int_{0}^{\pi/2} \sin^{102} x \, dx} ∫0π/2sin102xdx∫0π/2sin100xdx
If the integral above can be expressed as ab \dfrac abba, where aaa and bbb are coprime positive integers, find a+ba+ba+b.
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