AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2}|\sin t-\cos t| d t=\)
- A \(2(\sqrt{2}+1)\)
- B \(2(\sqrt{2}-1)\)
- C \(\sqrt{2}+1\)
- D \(\sqrt{2}-1\)
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} \\ = &…
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