Calculating Work Done by a Conservative Vector Field Along a Curve

[krtica]

If C is the curve given by r(t)=<1+3sin(t), 1+5sin^2(t), 1+5sin^3(t)>, 0≤t≤π/2 and F is the radial vector field F(x, y, z)=<x, y, z>, compute the work done by F on a particle moving along C.

Work= int (F dot dr)

If F is the potential function(?), do I integrate F with respect to each variable, then substitute the values of x, y, and z in r(t)? Would this then just be dotted into 1 since d/dt sin(t) is cos(t), which is 0 at π/2? Would my answer be something like (4^2/2)+(6^2/2)+(6^2/2)?

 

[gabbagabbahey]

Hint: d\textbf{r}=\textbf{r}&#039;(t)dt

 

[krtica]

So the integral is gross?

 

[gabbagabbahey]

No, the point of my hint is that you should differentiate your position function with respect to t, and then take the dot product with the position function and finally integrate the result. You'll have something like 6 terms to integrate, but they should all be straightforward.