Mathematics
ASSERTION

$$\int_{0}^{\pi }\sqrt{1-\sin ^{2}x}dx=0$$.

REASON

$$\int_{0}^{\pi }\cos xdx=0.$$


ANSWER

Assertion is incorrect but Reason is correct


SOLUTION
$$\int_{0}^{\pi }\sqrt{1-\sin ^{2}x}dx$$
$$=\int_{0}^{\pi }\left | \cos x \right |dx$$
$$=\int_{0}^{\frac{\pi}{2} }\cos xdx+\int_{\frac{\pi}{2}}^{\pi }-\cos xdx$$
$$=1+1=2$$
Hence, statement $$1$$ is false.
However, statement $$2$$ is true.
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Assertion & Reason Medium Published on 17th 09, 2020
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