Question

What is the value of Beta (1,1) =

Answer 1

X= 1

Y= 1

HOPE IT HELP YOU

MARK ME BRAINLEIEST

Answer 2

The value of β(1,1) = 1

Given :

β(1,1)

To find :

The value

Solution :

Step 1 of 2 :

Define Beta function

The Beta function is defined as

$\displaystyle \sf \beta(m,n) = \int\limits_{0}^{1} {x}^{m - 1} {(1 - x)}^{n - 1} \, dx$

Where m > 0 , n > 0

Step 2 of 2 :

Find the value of β(1,1)

Putting m = 1 , n = 1 we get

$\displaystyle \sf \beta(1,1)$

$\displaystyle \sf = \int\limits_{0}^{1} {x}^{1 - 1} {(1 - x)}^{1 - 1} \, dx$

$\displaystyle \sf = \int\limits_{0}^{1} {x}^{0} {(1 - x)}^{0} \, dx$

$\displaystyle \sf = \int\limits_{0}^{1} 1 \, dx$

$\displaystyle \sf = x\bigg| _{0}^{1}$

$\displaystyle \sf = 1 - 0$

$\displaystyle \sf = 1$

The value of β(1,1) = 1