Find the area of the region bounded by $y=\sqrt{|x|}$
and $5y = x+6$ by looking at where the curves intersected on a graph I got
$$\int_{-1}^4\Bigg[\frac{x+6}{5} – \sqrt{|x|}\Bigg]\,\, dx + \int_4^9 \Bigg[\frac{-(x+6)}{5} + \sqrt{|x|}\Bigg]\,\,dx$$ however I have no idea how to do an intergal with a square root like this and im not sure if im supposed to or messed up somewhere along the process to get to here. Im studying for my final so explanation of why and not just the solution would be appreciated.
Best Answer
Hint: $\int_{-1}^4 \sqrt{|x|}\,dx=\int_{-1}^0 \sqrt{-x}\,dx+\int_{0}^4 \sqrt{x}\,dx$
Note: $\sqrt{-x}$ exists since $x$ is negative in the domain $\int_{-1}^0$