I would realy appreciate your kind generous help with this one problem I'm working on in my Engineering Math Intro,
Evaluate $ \int_{c} xyz $ ds where C is the curve given by $ \vec r(t)=<t-2sint, t^2> $ and $ -3\le t \le 3 $
Seeing that the z function is zero in the provided parameterization, I couldn't help assuming the evaluation would go as follow:
$ \int_{-3}^{3} (t-2sint)(t^2)(0) \sqrt{(t-2sint)^2+(t^2)^2+(0)^2} dt$
which will bring $ \int_{-3}^{3} 0 dt =constant$
(I use the formula given in http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx)
Am I making a mistake?