Volume: base B is bounded by x=y^2+2, y=x-4, x-axis....

jlhannah

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The base B is located in the first quadrant and is bounded by x=y^2 + 2, y = x-4 and the x-axis. The solid S has the base B and has the cross sections perpendicular to B and parallel to the x-axis that are semicircles. Write and integral (a single integral) that gives the volume of the solid S.

I have an idea of what the shape looks like, but I don't know where to start for the integral!
 
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