# Thread: Find the force F = < 2x, e^y + z cos y,sin y > of a particle with line integrals

1. ## Find the force F = < 2x, e^y + z cos y,sin y > of a particle with line integrals

Given F = < 2x, e^y + z cos y,sin y >
Find the work done by the force in moving a particle from P(1, 0, 1) to Q(1, 2, −3) along the curved path given by C : r(t) =< 1 + sin πt, 2 sin(πt/2), 1 − 4t >, 0 ≤ t ≤ 1.

I tried plugging r into F but ended getting an extremely long and complex vector function to take the integral of. The hint said to think, so I assume I'm not supposed to brute force the integral. Is there any property of either F or r that will allow me to simplify my work?

I guess that "n"-looking thing is a $\pi$.

How sure are you that you are to evaluate it? Maybe the problem statement says just "set it up"?

3. Originally Posted by tkhunny

I guess that "n"-looking thing is a $\pi$.

How sure are you that you are to evaluate it? Maybe the problem statement says just "set it up"?
The problem says to evaluate it. However, if I find the curl of F, it is zero, so then the line integral would be zero?

4. That would work. I didn't get 0. I may have missed something.

5. Originally Posted by tkhunny
That would work. I didn't get 0. I may have missed something.
How did you set up your integral?

6. Originally Posted by Superyoshiom
How did you set up your integral?

7. Originally Posted by Superyoshiom
How did you set up your integral?
Yeah, that's not how this works. You first.