Q264 / 270 · NDA 2021 (Phase 2) · Mathematics

What is $\int_0^{\frac{\pi}{2}} e^{\ln (\cos x)} d x$ equal to?

  • A
    -1
  • B
    0
  • Correct answer
    C
    1
  • D
    2

Solution

$\begin{aligned} & \mathrm{I}=\int_0^{\pi / 2} e^{\ln (\cos x)} d x \\ & =\int_0^{\pi / 2} \cos x d x=[\sin x]_0^{\pi / 2}=\sin \frac{\pi}{2}-\sin 0=1\end{aligned}$

Hence, the correct answer is option: 'C'.

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