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AP EAMCET · Maths · Definite Integration

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

  1. A \(2(\sqrt{2}+1)\)
  2. B \(2(\sqrt{2}-1)\)
  3. C \(\sqrt{2}+1\)
  4. D \(\sqrt{2}-1\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(2(\sqrt{2}-1)\)

Step-by-step Solution

Detailed explanation

\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} \\ = &…