Find the area enclosed by the curves `x^2=y , y=x+2,

Explanation

To find the area enclosed by the curves \(x^2 = y\) and \(y = x + 2\), we will follow these steps:

### Step 1: Find the points of intersection
To find the area between the curves, we first need to determine where they intersect. We can do this by setting the equations equal to each other.

1. Set \(x^2 = x + 2\).
2. Rearranging gives us the equation:
\[ x^2 - x - 2 = 0 \]
3. Factor the quadratic:
\[ (x - 2)(x + 1) = 0 \]
4. Thus, the solutions are:
\[ x = 2 \quad \text{and} \quad x = -1 \]