Find the [[../Area between Curves|Area between Curves]] in the region below:
![[../../../00 Asset Bank/Pasted image 20240924161743.png|invert_B]]
$\huge \begin{align}
A &=
\int_{0}^{2} \pa{x+2}^{ \frac{1}{2}} \d x
-
\int_{{0}}^2 \pa{x+1}^{-1}\d x
\\&=
\frac{2}{3}\pa{2+2}^{\frac{3}{2}}
- \frac{2}{3}\pa{0+2}^{\frac{3}{2}}
-\pa{
\ln(2+1) - \ln(0+1)
}
\\&=
\frac{2}{3} \left(
4^{\frac{3}{2}} -
2^{\frac{3}{2}}
\right)
- \ln 3
\end{align}$