allery$\displaystyle\int_0^1 x^2(1-x)^3\, dx = ?$ (Beta function)
A$1/60$
B$1/12$
C$1/24$
D$1/720$
Answer & Solution
Correct answer: A. $1/60$
$B(m, n) = \int_0^1 x^{m-1}(1-x)^{n-1}dx = (m-1)!(n-1)!/(m+n-1)!$.
Here $m = 3$, $n = 4$: $B(3,4) = 2! \cdot 3! / 6! = 12/720 = 1/60$.
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