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

#### Superyoshiom

##### New member
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.

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[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

##### Moderator
Staff member

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

##### New member

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

##### Moderator
Staff member
That would work. I didn't get 0. I may have missed something.

#### Superyoshiom

##### New member
That would work. I didn't get 0. I may have missed something.
How did you set up your integral?

#### stapel

##### Super Moderator
Staff member
How did you set up your integral?