# Math Help - Integral and vector fields

1. ## Integral and vector fields

Hi,

having a problem with this one:

F is a vector field in R3 : F(x,y,z)=(yz,xz,xy)
\gamma is a curve : (x(t),y(t),z(t))=(cos t, sin t, t), 0<= t <= pi/4

find the integral of F over \gamma by using the curve's parameters.

if anybody can help me, thank you!

2. Standard curve integral:

where

3. I believe what you're looking for is

$\int_C {\bf F}\cdot {\bf dr} = \int_C yz dx + xzdy + xydz$

As the vector field is conservative then (the potential $\phi = xyz$) then the integral is

$\int_C yz dx + xzdy + xydz = \left. xyz \right|_{p_1}^{p_2}$ where $p_1$ and $p_2$ are the starting and finishing points.