Volume of a solid involving natural logs

I'm trying to solve the problem I've attached as a picture. I'm having some difficulty involving the step where I get to the integral from 1 to 3 of pi times (ln(4x)^2, because I don't really even know what that is. I thought it'd just be ln^2(4x) but then I have NO idea how to integrate that! I'd appreciate anyone who's willing to help.

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Originally Posted by fattydq

I'm trying to solve the problem I've attached as a picture. I'm having some difficulty involving the step where I get to the integral from 1 to 3 of pi times (ln(4x)^2, because I don't really even know what that is. I thought it'd just be ln^2(4x) but then I have NO idea how to integrate that! I'd appreciate anyone who's willing to help.

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First, remember that since you are using disks or washers for this problem and rotating about the y axis, your integral will need to be in terms of y.





So your integral should read:



See if that helps. Can you take it from here?

Here it is using shells. It is more complicated. I would suggest using washers.

Thanks man, I've got it now(Happy)