Integrating $\int_{C}F\cdot dr$ with F and r Given

[Xyius]

Homework Statement

The problem says to compute the following integral.

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

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..

$$\int^{1}_{0} (2t^2+1)e^{t^2}+3t^5e^{t^3}+3t^2e^{t^3}dt$$

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!

 

[Dick]

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??

 

[Xyius]

Ohh! Thats interesting! Yes let me do it now. :)

 

[Xyius]

Okay I got an answer of 3e. Here is my work.

http://img203.imageshack.us/img203/2750/photo1piq.jpg

Thanks a lot! :D!

 

[Dick]

Okay I got an answer of 3e. Here is my work.

http://img203.imageshack.us/img203/2750/photo1piq.jpg

Thanks a lot! :D!

That's a little hard to read. But I get 2e.

 

[Xyius]

Yeah sorry the resolution isn't too great. Anyway, I will post my work in detail later using Latex.

 

[Dick]

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?