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Question: Answered & Verified by Expert
$\int_{-\pi / 2}^{\pi / 2} \sin |x| d x$ is equal to
MathematicsDefinite IntegrationAP EAMCETAP EAMCET 2008
Options:
  • A $0$
  • B $1$
  • C $2$
  • D $\pi$
Solution:
2098 Upvotes Verified Answer
The correct answer is: $2$
Let
$$
\begin{aligned}
I & =\int_{-\pi / 2}^{\pi / 2} \sin |x| d x \\
& =2 \int_0^{\pi / 2} \sin x d x \\
& =2[-\cos x]_0^{\pi / 2} \\
& =2
\end{aligned}
$$

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