Volumes by Integration

Volumes by Integration: Shell Method Practice Problem Solution

2. Rotate the area bounded by the x and y axes and y=3-x² about the y axis and find the volume.

Here is the volume with the shell sketched in:

Now write the equation for the volume of the shell, dV:

                    dV=2pr*height*thickness

     

Write this in terms of  the variables, x and y:

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