Question

The integral `int dx/sqrt(9 - 4x^2)` is equal to ______.

Options

• `1/6 sin^-1((2x)/3) + c`

• `1/2 sin^-1((2x)/3) + c`

• `sin^-1((2x)/3) + c`

• `3/2sin^-1((2x)/3) + c`

Answer 1

The integral `int dx/sqrt(9 - 4x^2)` is equal to `underlinebb(1/2 sin^-1((2x)/3) + c)`.

Explanation:

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

`1/sqrt4 int 1/sqrt((3/2)^2 - x^2)`

using formula `1/sqrt (a^2 - x^2) = sin^-1  x/a + c`

`1/2 sin^-1  x/(3"/"2) + C`

`1/2 sin^-1  (2x)/3 + C`