Question

Find the area of the region bounded by curve $y^2=4x,x=1,\text{and}x=4$ and the x-axis in the first quadrant.

Answer 1

$\text{Area, A}={\int }_1^{4}ydx$
$={\int }_1^4\sqrt{4x}dx$
$=2{\int }_1^4\sqrt{x}dx$
$=2{\left(\frac{2}{3}{x}^{\frac{3}{2}}\right)}^4$
$=\frac{4}{3}(4^{\frac{3}{2}}-1^{\frac{3}{2}})$
$=\frac{28}{3}\text{units}$