Using Cylindrical Shells, find the volume of the solid generated by revolving the region bounded by the graphs y=x^2 and y=4 about the line x=2.

I'm posting my current work below this.

Thanks for all the help in advance!

Question

Using Cylindrical Shells, find the volume of the solid generated by revolving the region bounded by the graphs y=x^2 and y=4 about the line x=2.

I'm posting my current work below this.

Thanks for all the help in advance!

anonymous · Answer

This is the integral I've set up so far: $$2pi\int\limits_{-2}^{2}(2-x)(x^2)dx$$

abb0t · Answer

How did you get 2-x?

anonymous · Answer

That's where I went wrong. Thank you!

anonymous · Answer

I'm thinking that since we are moving the graph x^2 over 2 units to the right, that we would use x-2 as the average radius

nottim · Answer

so..we done?

anonymous · Answer

I'm still trying to figure the problem out with the abb0t's idea. I'm not sure if that's where I actually went wrong.

anonymous · Answer

2-x is there because we are shifting the graph over 2 units. From the y-axis to x=2 is a constant 2 units, but we must subtract the curve from the total radius.

abb0t · Answer

Well:
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