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

     

                 dV=2py(4-x)dy

Now substitute for x in terms of y, set limits, and integrate.

                dV=2py(4-y²)dy

               

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