Evaluate $\int_{0}^{\frac{\pi}{2}+1} \sin(x - \sin(x - \sin(x - \dots))) \mathrm{d}x$. Interpret t

Question

Evaluate $\int_{0}^{\frac{\pi}{2}+1} \sin(x - \sin(x - \sin(x - \dots))) \mathrm{d}x$. Interpret the nested expression as $\sin u$, where $u$ is the unique solution of $u+\sin u=x$ with $0\le u\le\pi/2$.

Accepted Answer

$\frac{3}{2}$

2023 MIT Integration Bee: Regular Season Q13

2023 MIT Integration Bee: Regular Season Q13

Solution:

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