# 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 $C=\partial S$.

Bill Space

16

## 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

Erdos

4.6K

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
- 424 views
- $8.00

### Related Questions

- Calculus Integral volume
- Prove that $\int _0^{\infty} \frac{1}{1+x^{2n}}dx=\frac{\pi}{2n}\csc (\frac{\pi}{2n})$
- Evaluate $\int ...\int_{R_n}dV_n(x_1^2 + x_2^2 + ... + x_n^2)$ , where $n$ and $R_n$ is defined in the body of this question.
- Line Integral
- Find the area under the graph of $y=\sin x$ between $x=0$ and $x=\pi$.
- Find the coordinates of the point $(1,1,1)$ in Spherical coordinates
- Compute the surface integral $ \int_S (∇ × F) \cdot dS $ for $F = (x − y, x + y, ze^{xy})$ on the given surface
- Integrate $\int x^2\sin^{-1}\left ( \frac{\sqrt{a^2-x^2} }{b} \right ) dx$