Question

The area under the curve $y=2\sqrt{x}$ bounded by the lines $x=0$ and $x=1$ is

• A. $\frac{4}{3}$
• B. $\frac{2}{3}$
• C. $1$
• D. $\frac{8}{3}$

Answer 1

The correct option is A $\frac{4}{3}$

$A=(0,0)$ , $B=(1,2)$ , $C=(1,0)$

$=2{\int }_0^1\sqrt{x}dx$

$[\frac{2x^{\frac{3}{2}}}{\frac{3}{2}}{]}_0^1$

$=\frac{4}{3}$