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int(dx)/(sqrt(9x-4x^2))equals(A) 1/9sin^...

`int(dx)/(sqrt(9x-4x^2))`equals(A) `1/9sin^(-1)((9x-8)/8)+C` (B) `1/2sin^(-1)((8x-9)/9)+C`(C) `1/3sin^(-1)((9x-8)/8)+C` (D) `1/2sin^(-1)((9x-8)/9)+C`

Text Solution

Verified by Experts

The correct Answer is:
b
`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`
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