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How can I find $\int{\sqrt{\left(b^2-1\right)x^2+1\over-x^2+1}}dx$?
I got this from the perimeter of an ellipse. I came up with the formula: arclength of f(x) for x from a to b=$\int_a^b\sqrt{f'(x)^2+1}dx$. Since an ellipse has the equation: $$\left({x-h\over ...
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1answer
145 views
how to calculate the double integral over the intersection of an ellipse and a circle
How to calculate the double integral of $f(x,y)$ within the intersected area?
$$f(x,y)=a_0+a_1y+a_2x+a_3xy$$
$a_0$, $a_1$, $a_2$, and $a_3$ are constants.
The area is the intersection of an ellipse ...
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2answers
2k views
Set up double integral of ellipse in polar coordinates?
How do you set up a double integral for an ellipse in polar coordinates without using Jacobian or Greens Theorem?
I can't seem to figure out what (or if) the limits of r can possible be.
$x = ...
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1answer
1k views
Moment of inertia of an ellipse in 2D
I'm trying to compute the moment of inertia of a 2D ellipse about the z axis, centered on the origin, with major/minor axes aligned to the x and y axes. My best guess was to try to compute it as:
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1answer
112 views
The probability of $Ax^2+Bxy+Cy^2 = 1$ defining an ellipse.
In Keith Kendig's paper, Stalking the Wild Ellipse (published in the American Mathematical Monthly, November 1995), he says that if $A, B, C$ are chosen at random, the probability that the Cartesian ...
