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

Integration Problem

  • Thread starter ACE_99
  • Start date
  • #1
35
0

Homework Statement


I'm just having a bit of trouble with where to start on this integral.

[tex]\int[1 - (r/0.11)]^1^/^5rdr[/tex]

The Attempt at a Solution



I've tried using integration by parts, "u" substitution and things like that but I dont seem to be getting anywhere with this. Any help would be greatly appreciated.
 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,346
4
Which substitutions did you try? Its obvious the stuff under the radical is giving you trouble, so why not try substituting it away.
 
  • #3
35
0
The first substitution that comes to mind is to let u = (1-(r/0.11)) so du = -1/0.11 dr. Rearranging for dr I get dr = -0.11du. If I sub this into the integral I still have an r in the equation.

From here I rearranged the expression u = (1-(r/0.11)) for r to get r = (1-u)(0.11). If I sub this into the integral I get

I = [tex]\int(u)^1^/^5(1-u)(0.11)(-0.11)du[/tex]
= [tex]\int(u)^1^/^5(1-u)(-0.0121)du[/tex]

It looks a bit better than before but I'm still stumped, hopefully the work I've done up to here is correct.
 
  • #4
Gib Z
Homework Helper
3,346
4
It is correct. Now just take the constant outside, and expand the brackets.
 
  • #5
35
0
If I do that then the integral becomes

I = -0.0121[tex]\int (u^1^/^5 - u^6^/^5)[/tex]
= -(0.0121)[(5/6)u6/5 - (5/11)u11/5]

So in order to get a solution I would also need to change the initial limits of integration using u = (1-(r/0.11)). If my initial limits of integration were 0 to 0.11 after subbing them into the equation for u my new limits of integration are from 1 to 0.
 
  • #6
Gib Z
Homework Helper
3,346
4
Yes that is correct. If you want to follow convention you'll have to introduce a negative factor and swap the new limits of integration to ensure the upper limit of integration is larger than the lower limit of integration.
 

Related Threads for: Integration Problem

  • Last Post
Replies
8
Views
1K
Replies
8
Views
1K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
1
Views
956
  • Last Post
Replies
1
Views
932
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
876
Top