The curve's function can be written:

`y=1/sqrt(4-x^2)`

This curve is completely above the `x`-axis for all values of `x` such that `-2 < x < 2`, as we can see in the graph below. (It's not defined for any other values of `x`).

Graph of 1/(sqrt(4-x^2))

So to find the required area (the shaded portion) we can simply integrate.

`A=int_0^1 1/(sqrt(4-x^2))dx`

`=[arcsin(x/2)]_0^1`

`=pi/6-0`

`=0.5236`