The integral _ /4 ^ 5 /4 (| t| t+| t| t ) ,dt has the value

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

The integral ∫π/45π/4(∣cos⁡t∣sin⁡t+∣sin⁡t∣cos⁡t) dt\int_{\pi/4}^{5\pi/4}\left(|\cos t|\sin t+|\sin t|\cos t\right)\,dt has the value (1) 0 (2) 12\frac{1}{2} (3) 12\frac{1}{\sqrt{2}} (4) 1

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