Tagged Questions
0
votes
1answer
37 views
Triple Integral Spherical Coordinates
So I have to compute the triple integral of this:
$\int\int\int \frac{1}{1+x^2+y^2+z^2}$ and it says the equation of the sphere is $ x^2 + y^2 + z^2 = z$ which is just an elongated sphere running ...
1
vote
1answer
48 views
How to integrate a vector function in spherical coordinates?
How to integrate a vector function in spherical coordinates?
In my specific case, it's an electric field on the axis of charged ring (see image below), the integral is pretty easy, but I don't ...
0
votes
1answer
155 views
Integration on the unit sphere
I have an integral on the unit sphere as follows.
$$I(\mathbf{s}_1, \mathbf{s}_2) = \int_{\mathbb{S}^2} f(\mathbf{x} \cdot \mathbf{s}_1)f(\mathbf{x}\cdot\mathbf{s}_2)d\mathbf{x} $$
where the ...
3
votes
0answers
151 views
Stokes' and Divergence Theorem Problems
I have 2 questions on stokes and divergence theorem each. I think I have done both and I just want to make sure that I did them correctly.
Question 1
Let C be the boundary of the surface ...
3
votes
1answer
83 views
Integration on a sphere
I have an integral at hand which has the form of
$$I = \int_{u\in \mathbb{S}^2} f(\mathbf{u}\cdot \mathbf{s}_1) f(\mathbf{u}\cdot \mathbf{s}_2) d\mathbf{u}$$
where $\mathbb{S}^2$ is the unit sphere ...
1
vote
1answer
63 views
Integral from Sphere to Disc
Suppose one has an integral of the form $\int_{S_1^{d-1}} f(\phi(v)) d \text{vol}_{S_1^{d-1}}(v)$. Here $S_1^{d-1}\subset \mathbb{R}^d$ is the unit sphere. Let $B_1^{d-1}\subset\mathbb{R}^{d-1}$ be ...
2
votes
1answer
173 views
What am I actually doing when I integrate using spherical coordinates in $\mathbb{R}^3$?
When learning vector fields and using Green's Theorem with the Jacobian to find the area of a level surface, I actually realized that most of the examples shown in my book would be much easier to ...
0
votes
2answers
600 views
Find the average value of this function
Find the average value of $e^{-z}$ over the ball $x^2+y^2+z^2 \leq 1$.
2
votes
1answer
262 views
integral of a spherically symmetric 3-dimensional function over all space
I'm very sorry because it may be a very basic question but I'm not able whether to solve it for sure, nor to find an answer in stackexchange or elsewhere.
I have to calculate
$ \int \int ...
3
votes
1answer
218 views
Monte carlo integration in spherical coordinates
I was playing around with writing a code for Montecarlo integration of a function defined in spherical coordinates. As a first simple rapid test I decided to write a test code to obtain the solid ...
