Evaluation of definite integrals

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Question

$\int_{0}^{π / 2} \sin x . d (x - [x]) =$

Moderate

Solution

$\int_{0}^{π / 4} \sin x d x = - {(\cos x)}_{0}^{π / 4} = \frac{1}{\sqrt{2}} + 1 = 1 - \frac{1}{1.4142} = 0.2929$

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