I've attached a picture of the graphs of these. I'd like to help you, but I'm not sure what you're asking. Is this a rotation problem? The area bounded by the curves is .
I hope this helps you in some way.
I am sorry I was not clear. The exact question is : FInd the double integral over the region S of x dA where S is the region bounded by the curves y = x^2/4, y = x, y =1 and y = 2 with x greater than or equal to 0.
Well, as y goes from to , x goes from to . (If , then ).
How about this: ?
Integrating with respect to gives you . Plugging in the bounds gives you .
Now the integral is .
You can integrate this by normal means to get . Plugging in the bounds gives you .
So is the answer you're looking for.