Question

Assertion :Area bounded by the curve $y=e^{x^3}$ between the ordinates x=a and x=b is ${\int }_a^b{e}^{x^3}dx$ Reason: $y=e^{x^3}$ is always 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

As $f\left(x\right)=y=e^{x^3}$
$\Rightarrow$ $f^{\prime }\left(x\right)=3x^2{e}^{x^3}$ which is increasing $\forall xϵR$
$\therefore$ Area bounded by the curve $y=e^{x^3}$ between the ordinates $x=a$ & $x=b$ is given by ${\int }_a^b{e}^{x^3}dx$
Assertion is correct and reason is also correct but it is not explanation of assertion.