Q217 / 270 · NDA 2023 (Phase 2) · Mathematics

What is $\int_0^{8 \pi}|\sin x| d x$ equal to?

  • A
    2
  • B
    4
  • C
    8
  • Correct answer
    D
    16

Solution

Since, $|\sin \mathrm{x}|$ is periodic function with period $\pi$ $\begin{aligned} & \text { So, } \int_0^{8 \pi}|\sin x| d x=8 \int_0^\pi|\sin x| d x \\ & \quad=8 \int_0^\pi|\sin x| d x=0 \\ & \quad=8(-\cos x)_0^\pi=8(+1+1)=16 \end{aligned}$

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

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