# Thread: Performing four separate line integrals

1. ## Performing four separate line integrals

S
is the surface of an open cube with faces defined by the planes

x
= 0, x = 2, y = 0, z = 0, z = 2. The open face is given by y = 2.
A vector field is given by
F = yz i + xyz j + xy k.
(should have a circle in the centre of it)
Perform the four separate line integrals in order to calculate
F.dr
c

where
dr is the element of the path C around the open end of the cube.

Can some one show me what this would look like and help me do the question

Thanks

2. Originally Posted by pip1690
S
is the surface of an open cube with faces defined by the planes

x
= 0, x = 2, y = 0, z = 0, z = 2. The open face is given by y = 2.
A vector field is given by F = yz i + xyz j + xy k.
(should have a circle in the centre of it)
Perform the four separate line integrals in order to calculate F.dr
c
where

dr is the element of the path C around the open end of the cube.

Can some one show me what this would look like and help me do the question

Thanks

1. Are you integrating clockwise or anti-clockwise?
2. Draw a diagram.
3. Integrating anti-clockwise, here's a starter:

Line 1: x = 2, $0 \leq y \leq 2$ and z = 0. On this line, dx = dz = 0, dy = dy.

The integral of F along this line boils down to $\int_0^2 (2) (y) (0) \, dy = 0$.

Line 2: y = 2, $0 \leq z \leq 2$ and x = 2. On this line, dx = dy = 0, dz = dz.

The integral of F along this line boils down to $\int_0^2 (2) (2) \, dz = 0$.

etc.