- #1

Gauss M.D.

- 153

- 1

## Homework Statement

Calculate the line integral:

F = <xz, (xy

^{2}+ 2z), (xy + z)>

along the curve given by:

1) x = 0, y

^{2}+ z

^{2}= 1, z > 0, y: -1 → 1

2) z = 0, x + y = 1, y: 1→0

3) z = 0, x-y = 1, y: 0 → -1

## Homework Equations

## The Attempt at a Solution

I don't think the problem is very difficult when just dividing the line integral into three parts, calculating each separately. But I want to be thorough to see if I got all the concepts.

I tried to draw the curve (see attachment) which made me realize a cone cut in half would be a capping surface, so we should be able to apply Stokes theorem. But I'm having trouble parametrizing it since we've basically dealt exclusively with very standard parametrizations.

I think that one parameter should be the height of the cone, h = [itex]\sqrt{y^{2}+z^{2}[/itex] running from 0 to 1 and the other should be the angle in the xz-plane running from 0 to [itex]\pi[/itex]. I'm just having trouble setting up the variable substitution. Can anyone give me a push?