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Previous Year Question (PYQs)
3
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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