# How do you find the volume of the solid if the region in the first quadrant bounded by the curves

How do you find the volume of the solid if the region in the first quadrant bounded by the curves $x=y-{y}^{2}$ and the y axis is revolved about the y axis?
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lydalaszq
The curve $x=y-{y}^{2}$ is a parabola that opens to the left. It has y intercepts 0 and 1
Using discs, we see that the radius is x or $y-{y}^{2}$, the thickness is dy, so the volume or a representative disc is
$\pi {r}^{2}d9y=\pi \left(y-{y}^{2}{\right)}^{2}dy$
Integrate from y=0 to y=1
${\int }_{0}^{1}\pi \left(y-{y}^{2}{\right)}^{2}dy=\pi {\int }_{0}^{1}\left({y}^{2}-3{y}^{3}+{y}^{4}\right)dy$
Which I believe is $\frac{17\pi }{60}$