Question

Assertion : ${\int }_{-2}^2\log \left(\frac{1+x}{1-x}\right)dx=0$
Reason : If $f$ is an odd function, then ${\int }_{-a}^{a}f(x)dx=0$.

• A. Assertion is correct, Reason is correct; Reason is a correct explanation for assertion
• B. Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion
• C. Assertion is correct, Reason is incorrect
• D. Assertion is incorrect, Reason is correct

Answer 1

Answer: (A)

$<br/>\begin{array}{l}<br/>{\int }_{-2}^2\log \left(\frac{1+x}{1-x}\right)dx=0\\ <br/>f(x)=\log \left(\frac{1+x}{1-x}\right)\\ <br/>f(-x)=\log \left(\frac{1-x}{1+x}\right)=-\log \left(\frac{1+x}{1-x}\right)=-f(x)\\ <br/>f\text{ is an odd function }\Rightarrow {\int }_{-a}^{a}f(x)dx=0<br/>\end{array}<br/>$
Both are true and Reason is correct explanation of Assertion.