Volumes by Integration

Volumes by Integration: Shell Method Practice Problem Solution

1. Determine the volume created by rotating the area bounded by the x axis, y=x^1/2, x=4 about the x axis.

Here is the volume. Try sketching in the shell.

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

            dV = circumference *height*thickness

            dV = 2p

r h dy = 2py(4-x)dy

Now find x in terms of y and substitute that into the equation.

            dV = 2p(4-y²)dy Since x=y²

Then set limits and integrate.

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