Question

Calculate the area under the curve $y=2\sqrt{x}$ included between the lines x = 0 and x = 1.

Answer 1

We have, y = $2\sqrt{x},x=0andx=1$

$\therefore$ Area of shaded region, $A={\int }_0^1\left(2\sqrt{x}\right)dx=2.{\left[\frac{x^{\frac{3}{2}}}{3}.2\right]}_0^1=2(\frac{2}{3}.1-0)=\frac{4}{3}squnits$