Question

Assertion :If $n>1$ then ${\int }_0^{\infty }\frac{dx}{1+x^n}={\int }_0^1\frac{dx}{{(1-x^n)}^{1/n}}$ Reason: ${\int }_a^{b}f\left(x\right)dx={\int }_a^{b}f(a+b-x)dx$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Given : If $(n>1){\int }_0^{\infty }\frac{dx}{(1+x^n)}={\int }_0^1\frac{dx}{(1-x^n{)}^{\frac{1}{n}}}$

${\int }_a^{b}f\left(x\right)dx={\int }_a^{b}f(a+b-x)dx$

Both assertion and reason are correct but reason is not a correct explanation for assertion.