Finding Volume of Solid with Perpendicular Rectangle Cross Sections

[physstudent1]

Homework Statement

The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the y-axis are rectangles of height y^3.

Use the information to solve for the volume of the solid.

Homework Equations

The Attempt at a Solution

I tried to find the base and height of the cross sections in terms of y, since the parabola is 2y^1/2 across for any height that is the base of the rectangular cross section is 2y^1/2 and the height will be y^3. This means the area of the cross section is the product of (2y^1/2)*y^3 =2*y^(7/2) then this integrated from 0 to 3 should give me the volume? I ended up getting 48/9 * 3^1/2 or 4/9 * 3^(9/2) could anyone verify this?

 

[physstudent1]

anyone?