Line Integral

1. Nov 29, 2005

Weatherkid11

Last edited by a moderator: Apr 21, 2017
2. Nov 29, 2005

amcavoy

$$\int_C\mathbf{F}\cdot d\mathbf{r}$$

$$\mathbf{F}=\left<x^4e^y,\,\ln{z},\,\sqrt{y^2+z^2}\right>$$

$$\mathbf{r}=\left<1+5t,\,2+2t,\,1+4t\right>;\quad 0\leq t \leq 1$$

Can you figure it out from here?

Last edited by a moderator: Apr 21, 2017
3. Nov 29, 2005

Weatherkid11

Last edited by a moderator: Apr 21, 2017
4. Nov 30, 2005

arildno

A few hints:
For the first term, use integration-by-parts, and for the third term, complete the square in the form: $K\sqrt{(t+a)^{2}+b}$, where K,a,b are appropriate constants. Dependent upon the sign of b, we may write $b=\pm{c}^{2}$ where c is some constant.

See if you manage to make the last few steps on your own..

Last edited by a moderator: Apr 21, 2017