Q115 / 160 · TS EAMCET 2018 (07 May Shift 1) · Mathematics

$\int_0^{1 / 2}|\sin 4 \pi x| d x=$

  • A
    $\pi-1$
  • B
    $\frac{2}{\pi}$
  • Correct answer
    C
    $\frac{1}{\pi}$
  • D
    0

Solution

$$ \begin{aligned} & \text { Let } I=\int_0^{1 / 2}|\sin 4 \pi x| d x \\ & =2 \int_0^{1 / 4}|\sin 4 \pi x| d x=2 \int_0^{1 / 4} \sin 4 \pi x d x \\ & =2\left[\frac{-\cos 4 \pi x}{4 \pi}\right]_0^{1 / 4}=\frac{1}{2 \pi}[-\cos \pi+\cos 0] \\ & =\frac{1}{2 \pi}[1+1]=\frac{1}{\pi} \end{aligned} $$

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

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