Question

What is the value of \(\int_0^1 x^5 (1-x)^6 dx\)?

(a) \(\frac{1}{12*11*10*9*8*7} \)

(b) \(\frac{1}{12*11*10*9*8} \)

(c) \(\frac{1}{12*11*10*9*8*7*6} \)

(d) \(\frac{1}{12*11*10*9*8*7*6*5} \)

This question was addressed to me in final exam.

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

Answer 1

Right option is (c) \(\frac{1}{12*11*10*9*8*7*6} \)

To elaborate: Here, m-1 = 5 which implies m=6 and n-1 = 6 which implies n=7.

\(\beta(6,7)= \frac{\Gamma(6)\Gamma(7)}{\Gamma(13)} = \frac{1}{12*11*10*9*8*7*6}. \)