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int(1)/(sqrt(9x-4x^(2)))dx is equal to...

`int(1)/(sqrt(9x-4x^(2)))dx` is equal to

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`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(1)/(sqrt(9x-4x^(2)))dx=(1)/(sqrt4)int(1)/(sqrt((9)/(4)x-x^(2)))dx`
`=(1)/(2)int(1)/(sqrt(-[x^(2)-(9)/(4)x+((9)/(8))^(2)]+((9)/(8))^(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`
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