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