#### Superyoshiom

##### New member

- Joined
- Sep 10, 2017

- Messages
- 10

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

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

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="]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]