if `int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(Bx)+C`, then A+B=

Options

A. `(9)/(4)`
B. `(19)/(4)`
C. `(3)/(4)`
D. `(13)/(12)`

Answer

D

Explanation

We have,
`int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(Bx)+C`
`implies(1)/(3)int(dx)/(sqrt(((4)/(3))^(2)-x^(2)))=Asin^(-1)(Bx)+C`
`implies(1)/(3)"sin"^(-1)(3x)/(4)+C=Asin^(-1)(Bx)+C`
On comparing both sides, we get
`A=(1)/(3) and B=(3)/(4)`
`thereforeA+B=(1)/(3)+(3)/(4)=(13)/(12)`