Question

If `int dx/sqrt(16 - 9x^2)` = A sin^–1 (Bx) + C then A + B = ______.

Options

• `9/4`

• `19/4`

• `3/4`

• `13/12`

Answer 1

If `int dx/sqrt(16 - 9x^2)` = A sin^–1 (Bx) + C then A + B = `underlinebb(13/12)`.

Explanation:

`int dx/sqrt(16 - 9x^2) = 1/3 int dx/sqrt((16/9) - x^2) = 1/3 int dx/sqrt((4/3)^2 - x^2)`

 = `1/3 sin^-1 [x/((4/3))] + C`

∴ A = `1/3` and B = `3/4`

∴ A + B = `1/3 + 3/4 = 13/12`