Question

If ${\int }_0^{\alpha }3x^{2}dx=8$, then the value of $\alpha$ is

• A. $0$
• B. $-2$
• C. $2$
• D. $\pm$ $2$

Answer 1

Answer: (C)

$2$

Given, ${\int }_0^{\alpha }3x^{2}dx=8$
$\Rightarrow 3{\int }_0^{\alpha }{x}^{2}dx=8$
$\Rightarrow 3{\left[\frac{x^3}{3}\right]}_0^{\alpha }=8$
$\Rightarrow [x^3{]}_0^{\alpha }=8$
$\Rightarrow [{\alpha }^3-0]=2^3$
$\Rightarrow \alpha =2$