Question

Find the area of the region bounded by the following curves, the $X-$axis and the given lines.
$y=\sqrt{6x+4},x=0,x=2$

Answer 1

Area $={\int }_0^2\sqrt{6x+4}={\frac{2{\left(\sqrt{6x+4}\right)}^3}{3\times 6}|}_0^2$

Area $=\frac{{\left(4\right)}^3}{9}-\frac{{\left(2\right)}^3}{9}=\frac{64-8}{9}=\frac{56}{9}$ sq units