Limit of this integral

  • #1
unscientific
1,734
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

  • integral-limits1.jpg
    integral-limits1.jpg
    40.4 KB · Views: 368

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,603
1,190

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.
 

Suggested for: Limit of this integral

  • Last Post
Replies
19
Views
203
Replies
2
Views
335
Replies
11
Views
309
Replies
2
Views
341
Replies
3
Views
385
  • Last Post
Replies
7
Views
353
Replies
5
Views
134
Replies
2
Views
205
  • Last Post
Replies
1
Views
227
Top