Hi Im having a bit of problem with volume btwn curves equations. Help is appreciated. Thanks. Volume formed by the solid with base enclosed ny the graphs of y=x^2 and y=2x with square cross-sections perpendicular to the a-axis.

Question

johan14th · Answer

I know the answer is 
limit(0 to 2)(2x-x^2)^2dx
I can't seem to understand how the (2x-x^2)^2 is determined.
I know for the area between curves is top -bottom (2x-x^2). However, how do you use that for the volume,is it the ^2 at the end?

mathmale · Answer

If I were doi ng this problem for myself, I'd begin by sketching the situation described.  Consider doing that.

mathmale · Answer

1.  At what x- and y- values do these two curves intersect?  This is how you'll determine your limits of integration.
2.  Did you mean "square cross sections parallel to the x-axis, or to the x-axis?
3.  If "parallel to the x-axis," you'll need to solve both of the given equations for x.
     Your expression for side length must be the difference of two x-values, which, in turn, are functions of y.
4.  Determine the limits of integration.  Sounds as tho' you'll be integrating with respect to y, from y=0 to y=??

johan14th · Answer

1. Okay so i know the limits are from 0 to 2 because of the intersection and bounded region
2. The problem says with square cross-sections perpendicular to the x axis.

johan14th · Answer

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