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TS EAMCET · Maths · Definite Integration

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

  1. A \(\pi-1\)
  2. B \(\frac{2}{\pi}\)
  3. C \(\frac{1}{\pi}\)
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{\pi}\)

Step-by-step Solution

Detailed explanation

\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}…