Help with a walk on an ellipse

  • Thread starter Thread starter octohydra
  • Start date Start date
  • Tags Tags
    Ellipse
octohydra
Messages
7
Reaction score
0
The problem is formally attached in the PDF. I did not see it fit to post my problem on the forum itself (sorry).

Any assistance is appreciated.

Thanks.
 

Attachments

Physics news on Phys.org
hey octohydra, welcome to PF, so you know it usually takes a while for attachments to clear
 
That is fine by me. I felt that this was the best way I could present the problem even if TeX is native to the forum.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Finding the largest ellipse that will fit in a polygon
Replies
4
Views
3K
Find locus of points near ellipse with some condition
Replies
5
Views
2K
Calc III: minimize the area of an ellipse
Replies
8
Views
3K
Why is b^2 = 4 for this ellipse?
Replies
6
Views
1K
Complex Analysis: Find Analytic Functions w/ |ƒ(z)-1| + |ƒ(z)+1| = 4
Replies
1
Views
1K
Line integral over vector field of a shifted ellipse
Replies
5
Views
3K
I Possible simple formula for ellipse circumference
Replies
6
Views
2K
Vector calculus for ellipse in polar coordinates
Replies
10
Views
3K
Simple multivariable problem w/ ellipse
Replies
1
Views
3K
I Difference between d/dt and d(theta)/dt? Why is it dr or ds/dt?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top