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Can you help me understand what a parabolic cylinder is in the context of this problem?

Asked by Mariah (25883points) July 5th, 2011

I have the most ridiculous calc homework this week. I’m going crazy trying to figure out this problem:

Evaluate the triple integral ∫∫∫ E (x+y) dV where E is bounded by the parabolic cylinder y=5x^2 and the planes z=x, y=20x, and z=0.

I don’t want solutions, mostly what I want is some help understanding the parabolic cylinder. I’m very confused because y=5x^2 is just the equation of a parabola; it’s two dimensional and I don’t know how it relates to a cylinder in any way. Am I supposed to extrude that parabola parallel to the z axis? If so, can you give me some pointers on how I’m supposed to develop an equation for the resulting three-dimensional shape?

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