Explain briefly why

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Explain briefly why, after replacing u=sin⁡xu=\sin x and adjusting the limits when computing ∫0πsin⁡x cos⁡(sin⁡x) dx\displaystyle \int_{0}^{\pi} \sin x\,\cos(\sin x)\,dx, it is not necessary to convert the antiderivative back to a function of xx before evaluating the integral.

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