<s>[INST] Find the number b such that the line y=b divides the region bounded by y=0 and y=4-x^2 into two regions with equal area. Find the number b such that the line y=b divides the region bounded by y=0 and y=4-x^2 into two regions with equal area. 
I know how to graph it out but I have no idea what to do after that.
 [/INST] The area between $y=4-x^2$ and $y=0$ is $\int_{-2}^{2}(4-x^2)\,dx = \frac{32}{3}$. 
We have to find some constant $b\in(0,4)$ such that the area between $y=4-x^2$ and $y=b$ equals $\frac{16}{3}$. That leads to the equation
$$ \int_{-\sqrt{4-b}}^{\sqrt{4-b}}(4-b-x^2)\,dx = \frac{16}{3} $$
and ultimately to $b=\color{red}{2(2-\sqrt[3]{2})}$.
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