# Integral problem

• Mar 1st 2010, 06:09 AM
Integral problem
If C has the parametric equation
$(x,y,z)=(t\cos(3t), t\sin(3t), \frac{t}{2}$ where $0\leq t\leq \pi$
How do you find $\int^ {}_{C} zds$
• Mar 2nd 2010, 05:21 AM
CaptainBlack
Quote:

If C has the parametric equation
$(x,y,z)=(t\cos(3t), t\sin(3t), \frac{t}{2}$ where $0\leq t\leq \pi$
How do you find $\int^ {}_{C} zds$

$ds=\sqrt{\left[\frac{dx}{dt}\right]^2+\left[\frac{dy}{dt}\right]^2+\left[\frac{dz}{dt}\right]^2}dt$

So:

$\int^ {}_{C} zds=\int_{t=0}^{\pi} \frac{t}{2}\sqrt{\left[\frac{dx}{dt}\right]^2+\left[\frac{dy}{dt}\right]^2+\left[\frac{dz}{dt}\right]^2}dt$

CB