# Stoke's Theorem

Find the work done by the vector field $F(x,y,z)=(-y,x,0)$ when displacing a particle on the boundary of the surface parameterized by $p(r,\theta)=(r(2+cos \theta)cos\theta, r(2+cos \theta)sin \theta, sin \theta)$ where $0 \leq r<1,0<\theta<2\pi$.

Rafalpha

39

## Answer

**Answers can only be viewed under the following conditions:**

- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

1 Attachment

Mathe

3.3K

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.

- answered
- 536 views
- $10.00

### Related Questions

- Let $z = f(x − y)$. Show that $\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=0$
- Evaluate $\int_C (2x^3-y^3)dx+(x^3+y^3)dy$, where $C$ is the unit circle.
- Find the absolute extrema of $f(x,y) = x^2 - xy + y^2$ on $|x| + |y| \leq 1$.
- Compute $\oint_C y^2dx+3xydy $ where where $C$ is the counter clickwise oriented boundary of upper-half unit disk
- Compute the surface integral $ \int_S (∇ × F) \cdot dS $ for $F = (x − y, x + y, ze^{xy})$ on the given surface
- Gauss's Theorem
- Show that $\int_\Omega \Delta f g = \int_\Omega f \Delta g$ for appropriate boundary conditions on $f$ or $g$
- Let $ X = x i+ y j+z k$, and $r=||X||$. Prove that $\nabla (\frac{1}{r})=-\frac{X}{r^3}.$

Low bounty!

Bounty seems too low.

The range of theta looks suspicious too, it probably goes from 0 to 2pi.

very suspicious. also, p(.) has only 2 components, how's that a surface in R^3?

Please double check the statement of your question. There seems to be typoes.

Ok, I changed it.

There is still a typo on the first component of p(r,theta)