Line Integrals: Compute 4xz + 2y dx

[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

 

[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*}<br /> x=2 + 2t \\<br /> y=1 - t \\<br /> z=2t \\<br /> 0&lt;t&lt;1 <br /> \end{align*}<br />

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...

 

[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.

 

[trancefishy]

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

 

[Hippo]

What a strange problem.