• Support PF! Buy your school textbooks, materials and every day products Here!

Triple integral

  • Thread starter kieranl
  • Start date
  • #1
24
0

Homework Statement


Sketch the solid E bounded by the cylinder x = y^2 and the planes z = 3 and x + z = 1, and write down its analytic expression. Then, use a triple integral to find the volume of E.

The Attempt at a Solution


Was wondering if someone could have a go at drawing this sketch? In mine, I thought i did it right but cant seem to obtain an enclosed surface. If x+z=1 was rather x-z=1 i would be able to but cant so far???
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,794
925
The plane x+ z= 1 crosses the plane z= 3 when x+ 3= 1 or the line x= -2, z= 3, y= t. It crosses the cylinder [itex]x= y^2[/itex] in the line [itex]x= t^2[/itex], [itex]y= t[/itex], [itex]z= 1- x= 1- t^2[/itex].

I wonder if you weren't confusing [itex]x= y^2[/itex] with the [itex]y= x^3[/itex].
 
  • #3
259
2
I don't think you NEED to graph this.

y=(plus/minus) sqrt(x)

If that helps.

The range is x>0, so sqrt(x) is real.

If x>0, which is on top, z=3 or z=1-x?


EDIt: Is there an upper bound on x?
 
  • #4
24
0
wat i have done is drawn the cylinder x = y^2 in the x-y plane and extended it along the z plane. Then i drew the z=3 plane and then drew a line z=1-x and it extended it along the y plane. But this does not end up enclosing a solid
 
  • #5
259
2
wat i have done is drawn the cylinder x = y^2 in the x-y plane and extended it along the z plane. Then i drew the z=3 plane and then drew a line z=1-x and it extended it along the y plane. But this does not end up enclosing a solid
You are right, I think. There must be an upper x-limit for this to be a solid. Maybe, you have accidentally skipped some information.
 

Related Threads for: Triple integral

  • Last Post
Replies
2
Views
977
  • Last Post
Replies
13
Views
737
  • Last Post
Replies
0
Views
670
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
Top