Tagged Questions
4
votes
2answers
87 views
How to solve this integral
Wolfram integrator is unable to solve this:
$$
\int_0^\pi \frac{1}{\sqrt {(a-\cos(t))^2+(b-\sin(t))^2+c^2}}\,\mathrm dt
$$
Any suggestions? Thanks!
2
votes
0answers
57 views
Calculating the integral $\int_{0}^{\pi /6}\sqrt{1-\left(\frac{R_s\sin \theta }{C_L}\right)^2} d\theta$
I want to integrate $I=\int\limits_{0}^{\pi /6}{\sqrt{1-{{\left( \frac{{{R}_{s}}\sin \theta }{{{C}_{L}}} \right)}^{2}}}d \theta}$.
I get incomplete elliptic integral $E(z\mid m)$ in the calculation by ...
1
vote
2answers
112 views
The integral relation between Perimeter of ellipse and Quarter of Perimeter
Ellipse Equation
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
$x=a\cos t$ ,$y=b\sin t$
$$L(\alpha)=\int_0^{\alpha}\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}\,dt$$
...
4
votes
1answer
160 views
Hypergeometric functions & integral
I'm having difficulty re-deriving a result a calculation from a paper. The integral is
$$\int_0^{2\pi} \int_0^{2\pi} ...
10
votes
2answers
229 views
Evaluating the elliptic integral $\int_{-\pi}^\pi\frac{dx}{\sqrt{(t-2\cos x)^2-4}}$
I have the following integral,
$$I(t)=\int_{-\pi}^\pi\frac{dx}{\sqrt{(t-2\cos x)^2-4}},$$
where $t>4$ is a real parameter. I know from messing around numerically and playing with Mathematica that
...
