# Elliptic Integral

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• Apr 2nd 2008, 02:41 PM
AceofSpades
Elliptic Integral
I would appreciate any help with evaluating this integral.

$
\int_0^\frac {\pi}{2} \sqrt{1 - e^2sin^2t}~dt

$

Where e is the eccentricity of an Ellipse

$
e^2 = \frac {a^2 - b^2}{a^2}
$
• Apr 2nd 2008, 03:06 PM
topsquark
Quote:

Originally Posted by AceofSpades
I would appreciate any help with evaluating this integral.

$
\int_0^\frac {\pi}{2} \sqrt{1 - e^2sin^2t}~dt

$

Where e is the eccentricity of an Ellipse

$
e^2 = \frac {a^2 - b^2}{a^2}
$

Since you are aware this is an elliptic integral, you know that this can not be done exactly, right? Are you asking for a good numerical method to do this?

-Dan
• Apr 2nd 2008, 03:26 PM
AceofSpades
Forgive me for my ignorance, I am an amateur at math.

Yes, I would like a numerical evaluation.
• Apr 2nd 2008, 05:08 PM
mr fantastic
Quote:

Originally Posted by AceofSpades
Forgive me for my ignorance, I am an amateur at math.

Yes, I would like a numerical evaluation.

Then you'll need a numerical value for the eccentricity.