Volume of Solid

  • #1

Homework Statement


The volume of the solid below the plane: z=2x and above the paraboloid z=x^2 + y^2.

I need help setting this one up, I can handle the evaluating.


The Attempt at a Solution



I just don't know.
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
Drawing a picture always helps. Try looking at a few contour lines.
 
  • #3
That's where i am having a problem... I believe you are suppose to set Z to 0. But then X^2 + y^2 = 0... So x and y =0??????
 
  • #4
Char. Limit
Gold Member
1,204
14
That is one of the contour lines, yes. It's also one of the endpoints on your integral. Where is the domain that you integrate over? Hint: It's where z1=z2, where z1=2x and z2=x^2+y^2.
 
  • #5
I'm assuming after you set z1=z2. You solve for each? Setting the other one to zero. So x=2 and y = 0?

Is it:

2 y...............2 y
S S 2x dxdy - S S x^2 + y^2 dxdy
0 0...............0 0
?
 
  • #6
Char. Limit
Gold Member
1,204
14
Well, consider that you're integrating over the circle (x-1)^2+y^2 = 1. Considering that, I might go into polar coordinates...
 
  • #7
thanks very much. I think i got it from here.
 
  • #8
Char. Limit
Gold Member
1,204
14
No problem. Glad I could help.
 

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