Thread: vector fields

Hello, I'm having trouble understanding work done by vector fields following a specific path. Here's a specific question I'm stuck on from my homework:

Find the work done by the force field F = ⟨x sin y , y⟩ on a particle that moves along the parabola y = x^2 from (−1,1) to (2,4).

thank you!

Hi upanddown.

I write on paper faster than typing LaTeX with an iPad. So here's a photo.



Hope this helps.

wow thank you!! this helped a whole lot. I was setting my t bound to the y values and not the x values which was giving me the wrong answer.

No problem. It was fun working one of those. Hadn't done one in a long time.

so if the vector r is already parametrized, how do I know how to parametrize the vector F?

for example, the vector <x,-y> if I already know r=<t^2,t^3>

oh nevermind, I just figured it out. thank you anyways!