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  4. Assertion: The area bounded by the circle y = sin x and y=- sin x from 0 to π is 3 sq. unit. Reason :The area bounded by the curves is symmetric about x -axis.

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Q. Assertion : The area bounded by the circle $y =\sin x$ and $y=-\sin x$ from $0$ to $\pi$ is 3 sq. unit.
Reason :The area bounded by the curves is symmetric about $x$ -axis.

Application of Integrals

Solution:

image
Shaded regions is the required area which is symmetric about $x$ -axis.
Required area $=2 \int\limits_{0}^{\pi} \sin x \,d x =2[-\cos y ]_{0}^{\pi}$
$=-2[(-1)-(1)]=-2(-2)=4$ sq. units.