Niven's theorem
= Niven's theorem
{wiki=Niven's_theorem}
Niven's theorem is a result in number theory that concerns the rationality of certain integrals. Specifically, it states that if \\( a \\) is a positive integer, then the integral \\\[ \\int_0^1 x^a (1 - x)^a \\, dx \\\] is a rational number and can be expressed in terms of the binomial coefficient.