# Beta function obtained by integration Calculator

## Calculates "Incomplete beta function Bx(a,b)" by the Gauss-Legendre quadrature."Complete beta function B(a,b)" can be obtained by "x=1".

 $\normal B_{x}(a,b)={\large\int_{\small 0}^{\hspace{25}x}}t^{a-1}(1-t)^{b-1}dt\\[10]$
 integrand: f(t,a,b)= variables a , b interval( , x ) [ partition n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ]
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Incomplete\ beta\ functions\ B_x(a,b),\ I_x(a,b)\\[10](1)\ Incomplete\ beta\ function\\\hspace{40}B_{x}(a,b)={\large\int_{\small 0}^{\hspace{25}x}}t^{a-1}(1-t)^{b-1}dt\\[10](2)\ Regularized\ incomplete\ beta\ function\\\hspace{40}I_{x}(a,b)={\large\frac{B_{x}(a,b)}{B(a,b)}}\\[10](3)\ Complete\ beta\ function\\\hspace{40}B(a,b)={\large\int_{\small 0}^{\hspace{25}\small 1}}t^{a-1}(1-t)^{b-1}dt\\$

Sending completion

To improve this 'Beta function obtained by integration Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?