I need to find the volume of a function x dA where S is bound by the curves y = x^2/4, y=x, y=1,and y=2 with x greater or equal to 0

I think x goes from 0 to 2 would y be between x and x^2/4???? Frostking

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- Mar 1st 2009, 09:15 PMFrostkingDouble integral region bound by curves
I need to find the volume of a function x dA where S is bound by the curves y = x^2/4, y=x, y=1,and y=2 with x greater or equal to 0

I think x goes from 0 to 2 would y be between x and x^2/4???? Frostking - Mar 1st 2009, 11:48 PMredsoxfan325
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. - Mar 2nd 2009, 06:03 AMFrostkingClarification of double integral problem
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.

- Mar 2nd 2009, 09:19 AMredsoxfan325
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.