Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilater triangles.

y=x^2, x=0, x=2, y=0
I know how to graph what is given, but I don't how to use the graph to do (a), (b), and (c). I have two other problems like this one. It would be great if you could show me how to do this one to do others like this one.

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  1. There are two ways to do this. Write the area of a crosssection as a function of height. dV= area dh, then integrate h from zero to y. Surely some examples are in your text, these are standard fare in a first year calc course.
    I don't think I can type out meaningful help here in ASCII.

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