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
tnanks .
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
tnanks .
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?