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if int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(B...

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

A

`(9)/(4)`

B

`(19)/(4)`

C

`(3)/(4)`

D

`(13)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(Bx)+C`
`rArr(1)/(3)(dx)/(sqrt(((4)/(3))-x^(2)))=Asin^(-1)(Bx)+C`
`rArr(1)/(3)sin^(-1)(3x)/(4)+C=Asin^(-1)(Bx)+C`
On comparing both sides, we get
`A=(1)/(3)andB=(3)/(4)`
`,." "A+B=(1)/(3)+(3)/(4)=(13)/(12)`
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