AP EAMCET · Maths · Definite Integration
If \(\int_0^{2 \pi}|x \sin x| d x=k \pi\), then \(k=\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\int_0^{2 \pi}|x \sin x| d x=k \pi\) ...(i) Let \(\mathrm{I}=\[\int_0^{2 \pi}|x \sin x| d x\) \(=\int_0^{2 \pi} x|\sin x| d x\]\{\because x>0\}\) \(=\left[\int_0^\pi x \sin x d x-\int_\pi^{2 \pi} x \sin x d x\right]\)…
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