The area enclosed by the curves y = sin x + cos x and y = | cos x – sin x | over the interval \left[\right. 0 , \textrm{ } \frac{\pi}{2} \left]\right. is

Engineering

Mathematics

Introduction to Area

Question

The area enclosed by the curves y = sin x + cos x and y = | cos x – sin x | over the interval $[0, \frac{π}{2}]$ is

$2 (\sqrt{2} + 1)$

$4 (\sqrt{2} - 1)$

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

$2 \sqrt{2} (\sqrt{2} + 1)$

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$∴$ The required area = $\int_{0}^{π / 2} (sinx + cosx) dx$

$= {(- cosx + sinx)}_{0}^{π / 2} - 2 {(sinx + cosx)}_{0}^{π / 2}$

= (0 + 1) – (– 1 + 0) – 2 $(\sqrt{2} - 1)$

$= 2 - 2 \sqrt{2} + 2$

$= 4 - 2 \sqrt{2} = 2 \sqrt{2} (\sqrt{2} - 1)$ .