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You know the experation for the area of a circle of radius R. It is Pi*R2.
But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major axis of length B? (These semi-major axes are half the lengths of, respectively, the smallest and largest diameters of the ellipse)
For example, the following is a standard formula for such an ellipse centered at the origin:
(x2/A2) + (y2/B2) = 1.
The area of such an ellipse is
Area = Pi * A * B ,
a very natural generalization of the formula for a circle!
Standard conventions in game theory Consider the given table: Y 3 -4 X -2 1
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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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