# Line Integrals

1. Apr 29, 2005

### PhysicsMajor

Greetings All,

I need serious help with this problem , well maybe several problems but I'll take it one at a time:

Compute the line integral of (4xz + 2y)dx where C is the line segment from (2,1,0) to (4,0,2).

Thanks

2. Apr 29, 2005

### trancefishy

$$\int_c f(x,y,z) ds = \int_a^b f(x(t), y(t), z(t)) \sqrt { \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 + \left( \frac{dz}{dt} \right)^2 }$$

so, you need to parametricize your line in space. par exemple:

\begin{align*} x=2 + 2t \\ y=1 - t \\ z=2t \\ 0<t<1 \end{align*}

those are *supposed* to be "less than or equal to" signs, but i never was able to find those.....

anyhow, you ought to be set to solve this puppy, unless you made it to here and collapsed....

Last edited: Apr 29, 2005
3. Apr 29, 2005

### Data

Well, he didn't have any annoying $ds$ to deal with.

All he needs to do is parameterize the curve and plug in for x, y, z, dx.

4. Apr 29, 2005

### trancefishy

oh, indeed, it is a dx. ecks, ess, they sound so similar in my noisy head...

5. Apr 29, 2005

### Hippo

What a strange problem.