find the definite integral of following – math.stackexchange.com

find the definite integral of following – math.stackexchange.com

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$$\int_0^{\pi}\lfloor\pi^2\cos^3x\rfloor\sin x\,dx$$ (where $\lfloor x \rfloor $ is the floor of $x$) I thought of breaking into required bounds but its too lengthy. Moreover i had to take cube root ...

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