Question

What is the value of $\int_0^1\frac{(y^5+y^2)}{(1+y)^9}  dy$?

(a) $\frac{1}{158}$

(b) $\frac{2}{167}$

(c) $\frac{1}{146}$

(d) $\frac{1}{168}$

The question was asked in class test.

The question is from Special Functions topic in chapter Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

Right choice is (d) $\frac{1}{168}$

Easy explanation: m-1 = 5 => m=6 and n-1 = 2 => n=3.

$\beta(6, 3) = \frac{\Gamma(6).\Gamma(3)}{\Gamma(6+3)}$

$= \frac{5!2!}{8!} = \frac{1}{168}.$