Integral problem

**pkrleads** · March 1st 2010, 05:09 AM

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 $\int^ {}_{C} zds$

**CaptainBlack** · March 2nd 2010, 04:21 AM

Originally Posted by pkrleads

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

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