Finding volume by using washer method and shell method

Find the volume of the solid generated by revolving the region bounded by y=2x, y=0, x=2, and x=4, around the y - axis.

I am having trouble getting the same answer using both the washer method and the shell method. For the washer method I get π(112/3), and with the shell method I get 2π(112/3). I can not figure out if I am doing one of them, or both of them wrong.

Re: Finding volume by using washer method and shell method

You don't say HOW you got those answers so I don't see how anyone can tell what you might have done wrong.

Re: Finding volume by using washer method and shell method

I meant to upload two photos, I will do that now, thanks

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Re: Finding volume by using washer method and shell method

Re: Finding volume by using washer method and shell method

The shells working is correct. For the washers, if you subtract one integral from another then that wants to be subtracting the integration of smaller discs (green here),

http://www.ballooncalculus.org/draw/misc/washers.png

from that of the larger. You can do the subtraction inside the integral (integrate all the washers, each one a blue minus green), but you do need a separate integral from 0 to 4 and from 4 to 8.