Question

Determine the area of the region enclosed by the curve $y=\sqrt{x+1}$ in $[0,4]$ and the $x$-axis and the lines $x=0,x=4.$

Answer 1

$\begin{array}{c}{\int }_0^4\sqrt{x+1}\\ =\frac{2}{3}{\left[{\left(x+1\right)}^{3/2}\right]}_0^4\\ =\frac{2}{3}\left[{\left(5\right)}^{3/2}-1\right]\end{array}$