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

Superyoshiom

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

[FONT=&quot]Given F = [/FONT][FONT=&quot]< 2x, e^y + z cos y,sin y >[/FONT][FONT=&quot]
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.

[/FONT]
[FONT=&quot]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?[/FONT]
 

tkhunny

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Please demonstrate.

I guess that "n"-looking thing is a \(\displaystyle \pi\).

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

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Please demonstrate.

I guess that "n"-looking thing is a \(\displaystyle \pi\).

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?
 

tkhunny

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

Superyoshiom

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stapel

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tkhunny

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