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int sqrt(9-4x^(2))dx=?...

`int sqrt(9-4x^(2))dx=?`

A

`(x)/(2)sqrt(9-4x^(2))+(9)/(4)sin^(-1)""(2x)/(3)+C`

B

`xsqrt(9-4x^(2))+(9)/(4)sin^(-1)""(2x)/(3)+C`

C

`(x)/(2)sqrt(9-4x^(2))-(9)/(4)sin^(-1)""(2x)/(3)+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`int sqrt(9-4x^(2))dx=2 int sqrt((9)/(4)-x^(2))dx=2 [(x)/(2)sqrt((9)/(4)-x^(2))+(9)/(8)sin ^(-1)""(x)/(((3)/(2)))]+C`
`=(x)/(2) sqrt(9-4x^(2))+(9)/(4)sin^(-1)""(2x)/(3)+C.`
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