Tagged Questions
4
votes
2answers
101 views
Help computing rational square root integral
Those integral techniques I thought I'd never need to remember are coming back to bite me. Is there a way to compute integrals of the form:
$$ \int_0^\infty \frac{1}{\sqrt{1 + a x^2 + b x^4}} dx $$
I ...
2
votes
1answer
55 views
An integral for the Earth's insolation
Consider the function
$$
[-\pi/2,\pi/2] \ni \theta \mapsto s_\beta(\theta) = \int_0^{2\pi}
\sqrt{ 1 - \left(\cos \theta \sin \beta \cos \gamma
- \sin \theta \cos \beta \right)^2} \, d \gamma
$$
for ...
3
votes
1answer
69 views
Can it possible to calculate this integral directly, probably concerning ellipti integral
A student asked me to help her calculating this problem: Assume the length $L$ of a curve is given, and the equation of the curve is
\begin{gather*}
y(x)=A \sin\Big(\pi x-\frac{\pi}{2}\Big), 0\leq ...
1
vote
0answers
101 views
Evaluating the average distance from a point in the unit disk to the disk
I am interested in finding the average Euclidean distance from a point $(x,y)\in\mathbb{D}_2$, the unit disk $\{(u,v):u^2+v^2\leq 1\}\subseteq\mathbb{R}^2$, to the disk $\mathbb{D}_2$. This amounts to ...
