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Using Shell Method to Evaluate Integrals

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis:
y=x^3, x=0, y=8

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In the shell method we divide the volume into concentric shells with their center aligned with the rotation axis.
In our case, the system looks ...

Solution Summary

This provides an example of using shell method to find volume in an attached pdf file.