Question

The value of `int_0^3dx/root  (9-x^2)` is ______.

Options

• `pi/6`

• `pi/4`

• `pi/2`

• `pi/18`

Answer 1

The value of `int_0^3dx/root  (9-x^2) " is " underlinebb(pi/2)`.

Explanation:

`int_0^3dx/root  (9-x^2)     ...[therefore1/root  (a^2-x^2) = sin^-1  x/a]`

I = `int_0^3dx/root  (3^2-x^2)`

I = `[sin^-1  x/3]_0^3`

`= [sin^-1  3/3 -sin^-1  0/3]`

`=pi/2`