`int_(0)^(1)x(1-x)^(9)dx`, किसके बराबर है ?

Options

A. `(1)/(110)`
B. `(1)/(132)`
C. `(1)/(148)`
D. `(1)/(240)`

Answer

A

Explanation

माना `l=int_(10)^(1)x(1-x)^(9)dx`
`=int_(0)^(1)(1-x)x^(9)dx " " [:'int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx]`
`=int_(0)^(1)(x^(9)-x^(10))dx=[(x^(10))/(10)-(x^(11))/(11)]_(0)^(1)`
`=(1/10 -1/11)=1/110 `