Triple Integral in Cylindrical Coordinates

  • Thread starter daveyman
  • Start date
  • #1
88
0

Homework Statement


Evaluate [tex]\int \int \int_E x^2 \, dV[/tex] where E is the solid that lies within the cylinder [tex]x^2+y^2=1[/tex], above the plane [tex]z=0[/tex], and below the cone [tex]z^2=4x^2+4y^2[/tex].


Homework Equations


In cylindrical coordinates, [tex]x^2+y^2=r^2[/tex] and [tex]x=r\cos{\theta}[/tex].


The Attempt at a Solution


I tried [tex]\int _0^{2\pi }\int _0^1\int _{-2r}^{2r}r^2 cos^2\theta\;\;r\;\;dzdrd\theta[/tex] but I must have messed up the bounds somehow.

Any ideas?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
252
… above the plane [tex]z=0[/tex]

I tried [tex]\int _0^{2\pi }\int _0^1\int _{-2r}^{2r}r^2 cos^2\theta\;\;r\;\;dzdrd\theta[/tex] but I must have messed up the bounds somehow.

Hi daveyman! :smile:

z goes from zero to 2r. :wink:
 
  • #3
88
0
Of course - it says it right in the problem :-) Thanks!
 

Related Threads on Triple Integral in Cylindrical Coordinates

Replies
8
Views
2K
Replies
1
Views
724
Replies
9
Views
4K
Replies
5
Views
6K
Replies
2
Views
727
Replies
4
Views
2K
Replies
7
Views
7K
Replies
2
Views
2K
Replies
7
Views
2K
Replies
3
Views
2K
Top