 The integrals we have discussed so far involve transcendental functions, but the gamma function also arises from integrals of purely algebraic functions.In particular, the arc lengths of ellipses and of the lemniscate, which are curves defined by algebraic equations, are given by elliptic integrals that in special cases can be evaluated in terms of the gamma function.The gamma function can also be used to calculate "volume" and "area" of -dimensional hyperspheres.