Assertion (A): _ -1 ^ 1 (x^3 + x + 2) dx = 0 . Reason (R): _ -a ^ a f(x) dx = cases 2…
Mathematics · Class 12 · CBSE — Integrals
Assertion (A): \(\displaystyle\int_{-1}^{1} (x^3 + \sin x + 2)\,dx = 0\).
Reason (R): \(\displaystyle\int_{-a}^{a} f(x)\,dx = \begin{cases} 2 \int_0^a f(x)\,dx, & \text{if } f(x) \text{ is even, i.e., } f(-x) = f(x) \\ 0, & \text{if } f(x) \text{ is odd, i.e., } f(-x) = -f(x) \end{cases}\)
- Both (A) and (R) are true and (R) is the correct explanation of (A).
- Both (A) and (R) are true but (R) is not the correct explanation of (A).
- (A) is true but (R) is false.
- (A) is false but (R) is true.
Answer
(D) (A) is false but (R) is true.
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