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.

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

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