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  4. ∫ limits0π / 2( cos x- sin x) ex d x=

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Q. $\int\limits_{0}^{\pi / 2}(\cos x-\sin x) e^{x} d x=$

Solution:

$\int\limits_{0}^{\pi / 2}[\cos x+(-\sin x)] e^{x} d x$
$=\left[e^{x} \cos x\right]_{0}^{\theta / 2}=-1$