`int(dx)/(sqrt(9x-4x^(2)))` बराबर है :

Options

A. `(1)/(9)sin^(-1)((9x-8)/(8))+C`
B. `(1)/(2)sin^(-1)((8x-9)/(9))+C`
C. `(1)/(3)sin^(-1)((9x-8)/(8))+C`
D. `(1)/(2)sin^(-1)((9x-8)/(9))+C`

Answer

B

Explanation

`int(1)/(sqrt(9x-4x^(2)))dx=(1)/(2)int(1)/(sqrt((9)/(4)x-x^(2)))dx`
`" "=(1)/(2)int(1)/(sqrt(((9)/(8))^(2)-(x-(9)/(8))^(2)))dx`
`" "=(1)/(2)sin^(-1)((x-(9)/(8))/((9)/(8)))+c`
`" "=(1)/(2)sin^(-1)((8x-9)/(9))+c`