Question

Assertion :${\int }_0^{\pi }\sqrt{1-{\sin }^{2}x}dx=0$. Reason: ${\int }_0^{\pi }\cos xdx=0.$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

${\int }_0^{\pi }\sqrt{1-{\sin }^{2}x}dx$
$={\int }_0^{\pi }\left|\cos x\right|dx$
$={\int }_0^{\frac{\pi }{2}}\cos xdx+{\int }_{\frac{\pi }{2}}^{\pi }-\cos xdx$
$=1+1=2$
Hence, statement $1$ is false.
However, statement $2$ is true.