Question

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

(a) ^1⁄2

(b) ^1⁄3

(c) ^1⁄4

(d) ^1⁄5

The question was asked in an interview for job.

My question is taken from Special Functions topic in section Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

The correct choice is (c) ^1⁄4

Easiest explanation: \(\int_0^∞ \frac{y^{1-1}}{(1+y)^5}  dy \)

n=1 and m + n = 5 which implies m=4.

\(\beta(4, 1) = \frac{\Gamma(4).\Gamma(1)}{\Gamma(4+1)} \)

\(\frac{3!0!}{4!} = \frac{1}{4} \).