Integrating a Line Integral Along a Curve with Given Boundaries

[Oakwater]

Homework Statement

∫(zdx+xdy+ydz)

along the curve C: x(t)= cos(t), y(t)= sin(t), z = 3t,

Boundaries are 0 and 2pi

Homework Equations

General integration and differentation.

The Attempt at a Solution

given the values I calculated that:

Using chain rule:

dx = -sintdt
dy = costdt
dz = 3dt

i then resubbed into the original equation to get:

∫(-3tsin(t)dt + cos^2(t)dt + 3sin(t)dt)

this is where I've got stuck, I attempted to integrate by parts the first term however it seems to get stuck in an endless loop, I'm not sure where to go from there.

 

[SteamKing]

Why don't you show us your work. It may be a simple problem to fix.

 

[tmiddlet]

The first and last terms of your integral should be easy to evaluate, the possibly tricky one is the middle term. The trick is to use the half-angle identity:
$$\cos^2 \theta = \frac{1 + \cos 2\theta}{2}$$