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**1. The problem statement, all variables and given/known data**

Let

**F**be a vector field

**F**= [-y

^{3}, x

^{3}+e

^{-y},0]

The path in space is x

^{2}+ y

^{2}= 25, z = 2.

My parametrization is

**r**(t) = [5cos(t),5sin(t),2]

**2. Relevant equations**

Line integral is the integral of

**F**(

**r**(t)) *

**r'**(t) dt, where here the asterisk * is for the dot product, not normal multiplication.

**3. 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,

Lee