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Study the Assertion and Reason and choose the correct option.
∫₋₁¹ (x³)/(cos x) dx = 0
Assertion: $\int_{-1}^1 \frac{x^3}{\cos x} dx = 0$
Reason: If $f(x)$ is a continuous function defined on $[0, a]$, then $\int_0^a f(x) dx = \int_0^a f(a-x) dx$
- aBoth Assertion and Reason are true, and Reason is the correct explanation of Assertion.
- bBoth Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
- cAssertion is true and Reason is false.
- dAssertion is false and Reason is true.
Answer
Answer
Official answer keyCorrect option: b
Answer: (b) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
$f(x) = \frac{x^3}{\cos x}$ is odd, because $f(-x) = -f(x)$, so $\int_{-1}^{1} \frac{x^3}{\cos x}dx = 0$. The Reason is a valid property of definite integrals, but it is not what makes this integral zero (the odd-function property does).