Question

I've got a Multivariable Calculus problem: I have to use Stoke's theorem to evaluate the integral of F*dr. F(x,y,z)=(x+y^2)i+(y+z^2)j+(z+x^2)k, where C is the triangle with vertices (1,0,0), (0,1,0), (0,0,1). C is oriented clockwise as viewed from above. I've gotten as far as crossing the gradient with F to get P, Q and R, as well as getting z=g(x,y)=1-x-y, partial of g wrt x= -1, partial of g wrt y= -1. I'm having a problem setting up the double integral; my solutions manual isn't doing what I thought I should do, and it doesn't explain itself. Please help if you can!

Answer 1

Find the curl of the vector field so you can apply stokes theorem.

Answer 2

which means find the cross product. I think it's \(curl\vec{F} \)\( = \nabla \times \vec{F}\) which means you also need
\(\frac{\partial}{\partial x}\) , \(\frac{\partial}{\partial y}\), and \(\frac{\partial}{\partial z}\)

Answer 3

hwoo. that took me FOREVER to write out!! trying to figure out how to write\(\vec{F}\), \(\nabla\), and \(\large \partial\)

Answer 4

Thanks! I'll definitely come to you if I have more calc problems.