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

Limit of this integral

  • #1
1,728
13

Homework Statement




The problem is attached in the picture.

The Attempt at a Solution



My question is, why can't the limits of ∫(dp) be from 0 to 1?

The shape is of the body is an inverted cone of angle 45 degree. Then isn't the question simply to find the integral of that function from p = 0 to p = 1, z = 0 to z = 1 and ∅ = 0 to ∅ = 2∏?

Since:

x = p cos∅
y = p sin∅
z = z


x2+y2 ≤ z2, 0 ≤ z ≤ 1

p2 ≤ z2

p ≤ z
 

Attachments

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,307
999

Homework Statement



The problem is attached in the picture.

The Attempt at a Solution



My question is, why can't the limits of ∫(dp) be from 0 to 1?

The shape is of the body is an inverted cone of angle 45 degree. Then isn't the question simply to find the integral of that function from p = 0 to p = 1, z = 0 to z = 1 and ∅ = 0 to ∅ = 2∏?
Doing what you suggest would be integrating over a right circular cylinder of radius 1 and height of 1.
 

Related Threads on Limit of this integral

Replies
24
Views
2K
Replies
4
Views
435
Replies
3
Views
1K
  • Last Post
Replies
0
Views
967
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
938
  • Last Post
Replies
15
Views
1K
  • Last Post
Replies
5
Views
946
  • Last Post
Replies
4
Views
1K
Top