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  4. The area under the curve y = | cos x - sin x |, 0 le x le (π/2), and above x-axis is :

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Q. The area under the curve $y = | \cos \, x - \sin \, x |, 0 \le x \le \frac{\pi}{2},$ and above x-axis is :

Application of Integrals

Solution:

$y = | \cos \, x - \sin x |$
image
Required area $= 2 \int\limits^{\pi /4}_{0} \left(\cos x - \sin x\right)dx $
$= 2\left[\sin x +\cos x\right]_{0}^{\pi/4} $
$= 2\left[\frac{2}{\sqrt{2}} - 1 \right] = \left(2\sqrt{2} -2\right) $ sq. units