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Calculus and Beyond Homework Help
Trouble visualizing what is going on. Volume of object
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[QUOTE="eumyang, post: 4490577, member: 222009"] The volume of a solid with a known cross section is basically [tex]{\int_a}^b A(x) dx[/tex], where A(x) represents the area of the cross section. I believe the attached graphic illustrates the problem. Imagine a square lying on its side, the side being the thin rectangle in the diagram. Now imagine a bunch of thin vertical rectangles going from left to right (from -r to r). The distance from the x-axis to the top of this particular rectangle is y. Then you know the length of this thin rectangle (= the length of the square cross section), which is 2y. The area of the square cross section is [tex]A = s^2[/tex] (s is the length of the side), so plug in 2y for s. Now, what does y equal in terms of x and r? Plug that in for y, and the resulting expression serves as the integrand for this problem. [/QUOTE]
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Calculus and Beyond Homework Help
Trouble visualizing what is going on. Volume of object
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