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)?
For each of the following vector fields F , decide whether it is conservative or not. Type in a potential function f (that is, ). If it is not conservative, type N. A.
A would be -7 +(-7), which is conservative? All of my answers are incorrect aside from B. I do not understand how D is incorrect though.
If or , then the field is conservative.