Question

Assertion :Area enclosed by the curve $y=e^{x^2}$ between the lines $x=a,x=b$ and $x-$axis is ${\int }_a^b{e}^{x^3}$ Reason: $e^{x^3}$ is an increasing function.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$\because y=e^{x^3}$
$\therefore \frac{dy}{dx}=e^{x^3}.3x^2>0$
$\Rightarrow y$ is an increasing function.
And area enclosed by the curve $y=e^{x^3}$ between the lines $x=a,x=b$ and $x-$axis is ${\int }_a^b{e}^{x^{3}dx}$