The area of the region bounded by the curve y | vedclass

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(D) The area $A$ of the region bounded by the curve $y = \cos x$,the $X$-axis,and the lines $x = -\frac{\pi}{2}$ and $x = \frac{\pi}{2}$ is given by t

Vedclass · Accepted Answer

$2$

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(D) The area $A$ of the region bounded by the curve $y = \cos x$,the $X$-axis,and the lines $x = -\frac{\pi}{2}$ and $x = \frac{\pi}{2}$ is given by the integral:$A = \int_{-\pi/2}^{\pi/2} |\cos x| \, dx$Since $\cos x \geq 0$ for $x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$,we have:$A = \int_{-\pi/2}^{\pi/2} \cos x \, dx$$A = [\sin x]_{-\pi/2}^{\pi/2}$$A = \sin(\frac{\pi}{2}) - \sin(-\frac{\pi}{2})$$A = 1 - (-1) = 1 + 1 = 2$Thus,the area is $2$ sq. units.

The area of the region bounded by the curve $y = \cos x$,$-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$ and the $X$-axis is . . . . . . sq. units.

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