Find the area bounded by the curves `x^(2)+y^(2)=4, x^(2)=-sqrt(2)y` and x = y.

Answer

To find the area bounded by the curves \( x^2 + y^2 = 4 \), \( x^2 = -\sqrt{2}y \), and \( x = y \), we will follow these steps:

### Step 1: Identify the curves
1. The equation \( x^2 + y^2 = 4 \) represents a circle with a radius of 2 centered at the origin.
2. The equation \( x^2 = -\sqrt{2}y \) can be rewritten as \( y = -\frac{x^2}{\sqrt{2}} \), which is a downward-opening parabola.
3. The equation \( x = y \) represents a line at a 45-degree angle through the origin.