Vector Integral

  • Thread starter Xyius
  • Start date
  • #1
508
4

Homework Statement


The problem says to compute the following integral.

[tex]\int_{C}F\cdot dr[/tex]
Where
[tex]F=<e^y,xe^y,(z+1)e^z> \ \ and \ \ r=<t,t^2,t^3>,0\leq t \leq 1[/tex]

2. The attempt at a solution
Basically when I plug everything in, I get an integral that CANT be solved. At first I thought to use Greens theorem, but I can't because it isn't two dimensional. When I plug everything in, I get..

[tex]\int^{1}_{0} (2t^2+1)e^{t^2}+3t^5e^{t^3}+3t^2e^{t^3}dt[/tex]

The only one I can immediate see is possible to do is the last term. MAYBE the second one, but definitely not the first one. (Not one part of it anyway.)

The first part of the question asked to find to potential function and I did that, I don't know if that would be in anyway relevant to this though.

Thanks!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
That's a good one! Had me scratching my head for a while. If you can get a potential function then you KNOW you can integrate it by using that. So no, you can't do e^(t^2) and you can't do t^2*e^(t^2). But you CAN do (2t^2+1)*e^(t^2). Wanna try and figure it out before I tell you??
 
  • #3
508
4
Ohh! Thats interesting! Yes let me do it now. :)
 
  • #4
508
4
Okay I got an answer of 3e. Here is my work.

http://img203.imageshack.us/img203/2750/photo1piq.jpg [Broken]

Thanks a lot! :D!!
 
Last edited by a moderator:
  • #5
Dick
Science Advisor
Homework Helper
26,263
619
Okay I got an answer of 3e. Here is my work.

http://img203.imageshack.us/img203/2750/photo1piq.jpg [Broken]

Thanks a lot! :D!!

That's a little hard to read. But I get 2e.
 
Last edited by a moderator:
  • #6
508
4
Yeah sorry the resolution isn't too great. Anyway, I will post my work in detail later using Latex.
 
  • #7
Dick
Science Advisor
Homework Helper
26,263
619
Yeah sorry the resolution isn't too great. Anyway, I will post my work in detail later using Latex.

You can check your answer using the potential expression, right? What does that say?
 

Related Threads on Vector Integral

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
874
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
8
Views
7K
  • Last Post
Replies
3
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
3
Views
531
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
7K
Top