Tagged Questions
1
vote
1answer
74 views
Stokes theorem problem to find alpha and beta so that I is independent of the choice of S
I have a question that I got half through but can't finish it. If anyone could help I would appreciate it.
Question: let C1 be the straight line from (-1,0,0) to (1,0,0) and C2 the semi circle ...
0
votes
0answers
58 views
Find area of a curvilinear triangle that includes hyperbolic functions
We were given this question in class and I tried to compute it and it looks to e pretty crazy. Can anyone take a look and let me know if I did it correctly... I would really appreciate it.
...
1
vote
2answers
122 views
Find area of a simple, smooth, closed curve lying in a plane
I was given this question in class and I assume it is a spin off of Green's theorem for finding the area of a closed curve $\lambda$ in 2D but expanded to 3D I believe. Anyways I am pretty confused ...
0
votes
0answers
55 views
Surface integral: Parametrize boundary $\delta \Sigma$ and determine $\int_{\delta \Sigma}f ds$ and $\int_{\delta \Sigma}f d \bf r$
Calculate the surface integrals $\iint_{\Sigma}f dS$ and $\iint_{\Sigma}f \bf dS$ where $$f(x,y,z)=(x^2+y^2+z^2)^2$$ and $$\Sigma=[x^2+y^2=z^2, y>=0, 0<=z<=2].$$
Parametrize the various ...
0
votes
1answer
64 views
Help me understand a surface integral question?
The question is:
Evaluate the surface integral:
$$
\iint\limits_S \, x^2yz\ \mathrm{d} S
$$
Where S is part of the plane z = 1 + 2x + 3y that lies above the rectangle [0,3] X [0,2]
I literally just ...
0
votes
2answers
171 views
What is the difference between surface area and scalar surface integrals?
What is the difference between the surface area of a paremetrized surface and the scalar surface integral of a function in $\mathbb{R}^3$? Are they not the same thing?
1
vote
0answers
856 views
Analytical calculation of the total surface of overlapping spheres
Let's say I have two spheres whose center's coordinates (cartesian) are
0,0,0
d,0,0
and both have radius R.
I want to analytically calculate the total surface ...
