Q59 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

\(\int_0^{\pi / 2}|\sin t-\cos t| d t=\)

  • A
    \(2(\sqrt{2}+1)\)
  • Correct answer
    B
    \(2(\sqrt{2}-1)\)
  • C
    \(\sqrt{2}+1\)
  • D
    \(\sqrt{2}-1\)

Solution

\(\begin{aligned} I= & \int_0^{\pi / 2}|\sin t-\cos t| d t=2 \int_0^{\pi / 4}(\cos t-\sin t) d x \\ & \left\{\because \int_0^{2 a} f(x) d x=2 \int_0^a f(x) d x \text { if } f(2 a-x)=f(x)\right\} \\ = & 2[\sin t+\cos t]_0^{\pi / 4} \\ = & 2\left[\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-0-1\right]=2(\sqrt{2}-1) \end{aligned}\) Hence, option (b) is correct.

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

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