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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: $\displaystyle \int_{-3}^{3} (x^3+5),dx = 30$ Reason R: $f(x)=x^3+5$ is an odd function. In the light of the above statements, choose the correct answer from the options given below:





Solution

$\displaystyle \int_{-3}^{3} x^3,dx = 0$ (odd function over symmetric limits) $\displaystyle \int_{-3}^{3} 5,dx = 5 \times 6 = 30$ So, $\displaystyle \int_{-3}^{3} (x^3+5),dx = 30$ ⇒ Assertion A is true. But $x^3+5$ is not an odd function (sum of odd and even function). So Reason R is false.


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