0 / 2 cos x ? e sin x ? d x is equal to:

Question

$\int_{0}^{π / 2} \cos x e^{\sin x} d x$ is equal to:

Smart Achievers · Accepted Answer

(2)

Ans. $e - 1$

Explanation :

Let $I = \int_{0}^{π / 2} \cos x e^{\sin x} d x$

Put $\sin x = t$

$\Rightarrow$ $\cos x d x = d t$

As $x \to 0$ , then $t \to 0$ ,

and as $x \to \frac{π}{2}$ , then $t \to 1$

$∴$ $I = \int_{0}^{1} e^{t} d t$ $= {[e^{t}]}_{0}^{1}$

$= e^{1} - e^{0}$

$= e - 1$

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