Q76 / 120 · VITEEE 2014 · Mathematics

$\int_{0}^{2 x}(\sin x+|\sin x|) d x$ is equal to

  • A
    0
  • Correct answer
    B
    4
  • C
    8
  • D
    1

Solution

$\int_{0}^{2 \pi}(\sin x+|\sin x|) d x$ $=\int_{0}^{\pi}(\sin x+\sin x) d x+$ $\quad \int_{\pi}^{2 \pi}(\sin x-\sin x) d x$ $=2 \int_{0}^{\pi} \sin x d x+0=-2 \int_{0}^{\pi} \cos x d x$ $=-2(\cos \pi-\cos 0)=-2(-1-1)=4$

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

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