hi:

have a problem solving this:

solved by using beta and gamma function

show that the area enclosed by the curve X^4+y^4=1

is {Gamma(1/4) }^2/2(sqrt(pi))

Could someone please help me (Flower)

tnanks .

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- Jan 18th 2010, 04:57 AMwesamplease help me the problem using beta and gamma
hi:

have a problem solving this:

solved by using beta and gamma function

show that the area enclosed by the curve X^4+y^4=1

is {Gamma(1/4) }^2/2(sqrt(pi))

Could someone please help me (Flower)

tnanks . - Jan 18th 2010, 06:50 AMHallsofIvy
Well, one way to do that, since this is a closed curve, is to change to polar coordinates: let and [tex]y= r sin(\theta). Now the equation of the curve is [tex]r^4 cos^4(\theta)+ r^4 sin^4(\theta)= 1 or and then the area is given by

.

.

Now, what are the**definitions**of the Gamma and Beta functions and how do they relate to that integral? - Jan 18th 2010, 07:10 AMwesam