Question

Assertion :${\int }_{-\pi /4}^{\pi /4}{x}^3{\sin }^{4}xdx\ne 0$ Reason: ${\int }_{-a}^{a}f\left(x\right)dx=0$ if $f(-x)=-f\left(x\right)$

• 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

For an odd function $f(-x)=-f\left(x\right)$ and

If $f\left(x\right)$ is an odd function then ${\int }_{-a}^{a}f\left(x\right)dx=0$.

Given $f\left(x\right)=x^{3}si{n}^{4}x$ is an odd function hence,

${\int }_{-\pi /4}^{\pi /4}{x}^{3}si{n}^{4}dx=0$.

So assertion is incorrect but reason is correct.