Question

If `int1/sqrt(16 - 25x^2) dx = a sin^-1(bx) + c`, then `a + 1/b` = ______ 

Options

• 1

• `7/12`

• `19/12`

• `9/12`

Answer 1

If `int1/sqrt(16 - 25x^2) dx = a sin^-1(bx) + c`, then `a + 1/b` = 1 

Explanation: 

Let I = `int1/sqrt(16 - 25x^2) dx`

= `int1/sqrt(4^2 - (5x)^2)` dx

= `1/5 sin^-1((5x)/4) + c`

Comparing with a sin^-1 (bx) + c, we get

a = `1/5`, b = `5/4`

∴ `a + 1/b = 1/5 + 4/5 = 1`