Question

If $A\left(x\right)={\int }_0^x{\theta }^{2}d\theta$
then value of $A\left(3\right)$ will be :

• A. 9
• B. 27
• C. 3
• D. 81

Answer 1

The correct option is A 9

$A\left(x\right)={\int }_0^x{\theta }^{2}d\theta$
= $[\frac{{\theta }^3}{3}{]}_0^x$
= $\frac{1}{3}{x}^3$
$\Rightarrow A\left(3\right)=\frac{1}{3}{3}^3$
= $\frac{1}{3}\times 3\times 3\times 3$
= $3\times 3$
= $9$
Thus, option A is correct