# Math Help - Path Integral

1. ## Path Integral

I'm having some issues with this path integral.
The vector field is F=<x,-y,-z>
The path is defined by c(t)=(sint, cost, t)
and t is from 0 to 3pi/2

How I have it set up, it turns out to be the integral of 2cos(t)sin(t) -t +1 from t=0 to t=3pi/2
because I plugged the c terms into the F, then did the dot product of that with the c prime terms

I solved this to be -cos^2(t)-((t^2)/2)+t,
then plugged in 3pi/2

but it was wrong
any ideas why?

Thanks

2. Originally Posted by Scottyd61891
I'm having some issues with this path integral.
The vector field is F=<x,-y,-z>
The path is defined by c(t)=(sint, cost, t)
and t is from 0 to 3pi/2

How I have it set up, it turns out to be the integral of 2cos(t)sin(t) -t +1 from t=0 to t=3pi/2 Mr F says: This is wrong. If you show all the details of your calculation the mistake(s) you made can be pointed out.

because I plugged the c terms into the F, then did the dot product of that with the c prime terms Mr F says: Correct method but you obviously have not done it correctly. See above.

I solved this to be -cos^2(t)-((t^2)/2)+t,
then plugged in 3pi/2

but it was wrong
any ideas why?

Thanks
..

3. Do you want $\int \bf{F}\cdot\bf{dr}$?

$\bf{F}\cdot\bf{dr}=<\sin t,-\cos t,-t>\cdot <\cos t,-\sin t,1>dt$

$=(2\sin t\cos t -t)dt$

and $\int (2\sin t\cos t-t)dt=\sin^2 t-t^2/2+C$