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Question: Answered & Verified by Expert
$\int_0^{\pi / 4} \cos x e^{\sin x} d x$ is equal to
MathematicsDefinite IntegrationBITSATBITSAT 2023 (Memory Based Paper 2)
Options:
  • A $e+1$
  • B $e-1$
  • C $e$
  • D $-e$
Solution:
1319 Upvotes Verified Answer
The correct answer is: $e-1$
Suppose, $I=\int_0^{\pi / 2} \cos x e^{\sin x} d x$
Let $\sin x=t \Rightarrow \cos x d x=d t$
$x \rightarrow 0 \Rightarrow t \rightarrow 0$
and $x \rightarrow \frac{\pi}{2} \Rightarrow t \rightarrow 1$
So $I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e-1$

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