Find the volume of the following solid S:
The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 2). Cross-sections perpendicular to the y-axis are semicircles.
So far I got the x point on the curve so that the diameter of the semicircle is -3/2y+3 and then to get the radius I got it by dividing the diameter by 2 which I got -3/4y+3/2 and then to find the volume of it its the integral of 1/2pi(r)^2= integral 1/2pi(-3/4y+3/2)^2= 1/2pi integral (-9/16y^2-18/16y+9/4) then when I integrated it I got 1/2pi(-3/16y^3-9/16y^2+9/4y) evaluated at 2 and 0 for the limits of integration and I got 3/4-0 which would equal 3/8pi and that wasn't the correct answer, I'm not sure exactly where I messed up