Question
If $f(x, y)=100(y+1)$ represents the population density of a planar region on Earth, where $x$ and $y$ are measured in miles, find the number of people in the region bounded by the curves $x=y^{2}$ and $x=2 y-y^{2}$
Step 1
To do this, we set the two equations equal to each other and solve for $y$: \[y^{2}=2 y-y^{2}\] This simplifies to $2y^{2}=2y$, which further simplifies to $y^{2}=y$. The solutions to this equation are $y=0$ and $y=1$. These are the $y$-values where the two curves Show more…
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