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$\int_{0}^{\pi / 2} e^{\sin } x \cos x d x$ is equal to
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Verified Answer
The correct answer is:
$e-1$
$\int_{0}^{\frac{\pi}{2}} e^{\sin x} \cdot \cos x d x$
Let $\sin x=t \Rightarrow \cos x \cdot d x=d t$
$\therefore \int_{0}^{\frac{\pi}{2}} e^{\sin x} \cdot \cos x d x=\int_{0}^{1} e^{t} . d t$
$=\left(e^{t}\right)_{0}^{1}=e^{1}-e^{0}=e-1$
Let $\sin x=t \Rightarrow \cos x \cdot d x=d t$
$\therefore \int_{0}^{\frac{\pi}{2}} e^{\sin x} \cdot \cos x d x=\int_{0}^{1} e^{t} . d t$
$=\left(e^{t}\right)_{0}^{1}=e^{1}-e^{0}=e-1$
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