Mathematics
ASSERTION

$$\displaystyle \int_{-\pi /4}^{\pi /4}x^{3}\sin ^{4}xdx\neq 0$$

REASON

$$\displaystyle \int_{-a}^{a}f\left ( x \right )dx=0$$ if $$f\left ( -x \right )=-f\left ( x \right )$$


ANSWER

Assertion is incorrect but Reason is correct


SOLUTION
For an odd function $$f(-x)=-f(x)$$ and

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

Given $$f(x)=x^3sin^4x$$ is an odd function hence,

$$\int_{-\pi/4}^{\pi/4}x^3sin^4dx=0$$.

So assertion is incorrect but reason is correct.

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Assertion & Reason Medium Published on 17th 09, 2020
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