Mathematics

# Evaluate: $\int\limits_0^{\dfrac{\pi }{2}} {\cos x\;{e^{\sin x}}\;{\text{dx}}}$

##### SOLUTION
$\displaystyle I = \int_{0}^{\pi /2} \cos\,x \,e^{\sin\,x}dx$

Let $\sin\,x = t$           $x = \pi /2$     $t = 1$

$\Rightarrow \cos\ x \ dx = dt$    $x = 0$   $t = 0$

$\displaystyle \Rightarrow I = \int_{0}^{1} e^{t}dt$

$= [e^{t}]_{0}^{1} = e-1$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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