Find the volume of the solid enclosed by the parabolic cylinder y=x^2 and the planes z=3y, z=2+y

Question

anonymous · Answer

Would it be: $$\int\limits_{}^{}\int\limits_{R}^{}(2+y)-3ydydx?$$But I'm not sure about the limits of integration and where y=x^2 comes in

turingtest · Answer

|dw:1352589692588:dw|

anonymous · Answer

Ok, so one bound is 1 to 3! What about the other?

turingtest · Answer

|dw:1352589774627:dw|

anonymous · Answer

But, if I just needed to do that, then I would be using x^2 at all?

anonymous · Answer

*wouldn't

turingtest · Answer

you still gotta integrate that over D, make it a function of y

anonymous · Answer

What do you mean? Haven't we found the bounds of integration and the function?

turingtest · Answer

what function are you using?

anonymous · Answer

2+y-3y? This problem is one from a section and the instructions at the top of the exercise list say to find the volume of the solid by subtracting the two volumes.

turingtest · Answer

the way I figured it the function we would use here would be sqrt(y)... or maybe 2sqrt(y) to make up for the - part
I'm actually a bit unsure

anonymous · Answer

Looking, I found http://answers.yahoo.com/question/index;_ylt=Ai0ISdvTCJ3r9BaHMY0FaOnsy6IX;_ylv=3?qid=20110120094838AAietqu and http://answers.yahoo.com/question/index?qid=20081114141004AAOjUd4, but it looks like they have different bounds of integration

turingtest · Answer

the first one seems to be your exact problem

anonymous · Answer

Could you explain how they got the limits for those?

turingtest · Answer

I don't understand the dA=2xdy part

anonymous · Answer

Ha, I'm not sure I understand much of it either!