$\int_{-\pi / 2}^{\pi / 2} \sin |x| d x$ is equal to

$\int_{-\pi / 2}^{\pi / 2} \sin |x| d x$ is equal to
  1. $0$
  2. $1$
  3. $2$
  4. $\pi$

Solution

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} $

Asked in: AP EAMCET 2008

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