# Stokes' theorem $\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$ verification

$$\int_S \nabla \times F \cdot dS= \int_C F\cdot dr$$

where $F=(2x,3xy^2,5z)$ where $S$ is the surfce of the paraboloid

\[z=4-x^2-y^2, z\geq 0\]

and $C=\partial S$.

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

1 Attachment

The answer is accepted.

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

- answered
- 176 views
- $8.00

### Related Questions

- Find the extrema of $f(x,y)=x$ subject to the constraint $x^2+2y^2=2$
- Is $\int_0^1 \frac{\cos x}{x \sin^2 x}dx$ divergent or convergent?
- Evaluate $\int \sin x \sqrt{1+\cos x} dx$
- Integral of trig functions
- Find the coordinates of the point $(1,1,1)$ in Spherical coordinates
- Riemann Sums for computing $\int_0^3 x^3 dx$
- Convex subset
- In what direction the function $f(x,y)=e^{x-y}+\sin (x+y^2)$ grows fastest at point $(0,0)$?