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Math Help - [SOLVED] Integration: Volume of Solids

  1. #1
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    [SOLVED] Integration: Volume of Solids

    I am having a tough time understanding how to get the cross sectional areas which you integrate:

    The base of a solid is the region bounded by y=x^{2} and y=4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are (a)squares; (b)semicircles; (c)equilateral triangles

    the answer to (a) shows \int(4-x^{2})^{2}\(from -2 to 2) from what I have tried to understand, the reason it's squared is because its a square so you are multiplying 2 equal lengths but I don't understand how 4-x^{2} would be the distance in the bounded region.

    Thanks in advance.
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  2. #2
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    what is the vertical distance between one point on the line y = 4 and the point directly below it on the parabola y = x^2 ?
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  3. #3
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    hahah yeah it would be [tex]4-x{2}[\math] I was thinking about horizontal distance lol. Thanks for helping me put things into proper perspective
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