Question

$\underset{x\to 0}{lim}\frac{{\int }_0^{x^2}\left(\sin \sqrt{t}\right)dt}{x^3}$ is equal to :

• A. $\frac{2}{3}$
• B. $0$
• C. $\frac{1}{15}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{2}{3}$

$\underset{x\to 0}{lim}\frac{{\int }_0^{x^2}\left(\sin \sqrt{t}\right)dt}{x^3}$
$=\underset{x\to 0}{lim}\frac{\sin |x|2x}{3x^2}=\frac{2}{3}$