Let F be a vector field F = [-y3, x3+e-y,0]
The path in space is x2 + y2 = 25, z = 2.
My parametrization is r(t) = [5cos(t),5sin(t),2]
Line integral is the integral of F(r(t)) * r'(t) dt, where here the asterisk * is for the dot product, not normal multiplication.
The Attempt at a Solution
The way I have always done line integrals is to express the field F in terms of r(t), or F(r(t)), then dot that with r'(t), then integrate. But this method leads to terms like cos(t)e-5sin(t).... so I am thinking my old way of doing these line integrals isn't going to work here. If you would like me to post my attempt at a solution I will, but hopefully someone can help me do this line integral in a different way or point out an error. It's been a little over a year since I've done line integrals and I'm a little rusty. Thanks in advance for the help,