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please help me the problem using beta and gamma
Well, one way to do that, since this is a closed curve, is to change to polar coordinates: letOriginally Posted by wesam
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 .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
![\int_{\theta= 0}^{2\pi}\int_{r=0}^\frac{1}{\sqrt[4]{cos^4(\theta)+ sin^4(\theta)}} r drd\theta](http://latex.codecogs.com/png.latex?\int_{\theta= 0}^{2\pi}\int_{r=0}^\frac{1}{\sqrt[4]{cos^4(\theta)+ sin^4(\theta)}} r drd\theta)
![= \int_{\theta= 0}^{2\pi}\frac{1}{2(\sqrt[4]{cos^4(\theta)+ sin^4(\theta)})^2} d\theta](http://latex.codecogs.com/png.latex?= \int_{\theta= 0}^{2\pi}\frac{1}{2(\sqrt[4]{cos^4(\theta)+ sin^4(\theta)})^2} d\theta)
.
.
Now, what are the definitions of the Gamma and Beta functions and how do they relate to that integral?
