Question

Why is $d \vec S = (\frac{\partial r}{\partial u}) \times (\frac{\partial r}{\partial v}) \ du\ dv$ and not $=(\nabla F)\ du \ dv$ on $S$?

score 130 · Answer 1 · 2018-04-02 08:35:39

130

Views

Why is $d \vec S = (\frac{\partial r}{\partial u}) \times (\frac{\partial r}{\partial v}) \ du\ dv$ and not $=(\nabla F)\ du \ dv$ on $S$?

Published on 02 Apr 2018 - 8:35

score 228 · Answer 2 · 2018-04-04 16:21:42

228

Views

Surface integral of spherical shell in a $e^{-x^2}$ field

Published on 04 Apr 2018 - 16:21

score 60 · Answer 3 · 2018-04-04 22:56:52

60

Views

Integral $\int_{0}^{a_{j}} \int_{0}^{b_{j}} \frac{1}{\sqrt{(x-x_{i})^{2}+(y-y_{i})^{2}+z_{i}^{2}}} \, dy \, dx$

Published on 04 Apr 2018 - 22:56

score 315 · Answer 4 · 2026-03-22 09:58:13

315

Views

Surface integral over the surface of a sphere

Published on 22 Mar 2026 - 9:58

score 1.9k · Answer 5 · 2026-03-25 03:02:58

1.9k

Views

Compute the surface area of the unit sphere $x^2+y^2+z^2=1$

Published on 25 Mar 2026 - 3:02

score 48 · Answer 6 · 2018-04-09 13:27:21

48

Views

Is this a correct way to solve this surface integral?

Published on 09 Apr 2018 - 13:27

score 402 · Answer 7 · 2026-03-23 04:00:09

402

Views

How to evaluate surface integral of a cylinder above a square

Published on 23 Mar 2026 - 4:00

score 1.5k · Answer 8 · 2018-04-19 16:32:13

1.5k

Views

solve surface integral of a scalar function using divergence theorem

Published on 19 Apr 2018 - 16:32

score 113 · Answer 9 · 2026-03-21 18:03:37

113

Views

Euler's equation

Published on 21 Mar 2026 - 18:03

score 534 · Answer 10 · 2026-03-22 20:18:56

534

Views

Investigate maxima of Gaussian integral over sphere.

Published on 22 Mar 2026 - 20:18

score 2.3k · Answer 11 · 2018-04-28 20:17:22

2.3k

Views

Find the area of the cap cut from the sphere by the cone implicitly and explicitly

Published on 28 Apr 2018 - 20:17

score 123 · Answer 12 · 2026-03-22 21:17:25

123

Views

Area of plane $2x+y+2z=2$ in the cylinder $x^2+y^2=16$

Published on 22 Mar 2026 - 21:17

score 571 · Answer 13 · 2026-03-25 00:07:41

571

Views

Calculate the flux through cylinder $x^2+y^2 \leq 9$

Published on 25 Mar 2026 - 0:07

score 415 · Answer 14 · 2018-05-02 04:13:09

415

Views

Evaluate Surface integral: $\vec F=y{\hat i}+x{\hat j}+zy{\hat k}$, S is part of $z=x^2+y^2$ above $z=1$. Assume S has an upwards orientation.

Published on 02 May 2018 - 4:13

score 2.5k · Answer 15 · 2026-03-22 09:44:10

2.5k

Views

Integral over a surface in 4-dimensions

Published on 22 Mar 2026 - 9:44

List Question

Why is $d \vec S = (\frac{\partial r}{\partial u}) \times (\frac{\partial r}{\partial v}) \ du\ dv$ and not $=(\nabla F)\ du \ dv$ on $S$?

Surface integral of spherical shell in a $e^{-x^2}$ field

Integral $\int_{0}^{a_{j}} \int_{0}^{b_{j}} \frac{1}{\sqrt{(x-x_{i})^{2}+(y-y_{i})^{2}+z_{i}^{2}}} \, dy \, dx$

Surface integral over the surface of a sphere

Compute the surface area of the unit sphere $x^2+y^2+z^2=1$

Is this a correct way to solve this surface integral?

How to evaluate surface integral of a cylinder above a square

solve surface integral of a scalar function using divergence theorem

Euler's equation

Investigate maxima of Gaussian integral over sphere.

Find the area of the cap cut from the sphere by the cone implicitly and explicitly

Area of plane $2x+y+2z=2$ in the cylinder $x^2+y^2=16$

Calculate the flux through cylinder $x^2+y^2 \leq 9$

Evaluate Surface integral: $\vec F=y{\hat i}+x{\hat j}+zy{\hat k}$, S is part of $z=x^2+y^2$ above $z=1$. Assume S has an upwards orientation.

Integral over a surface in 4-dimensions

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