Using integration find the area of the region bounded by the curves `y=sqrt(4-x^2),x^2+y^2-4x=0` and the x-axis.

Explanation

To find the area of the region bounded by the curves \( y = \sqrt{4 - x^2} \) and \( x^2 + y^2 - 4x = 0 \) along with the x-axis, we will follow these steps:

### Step 1: Identify the curves
The first curve \( y = \sqrt{4 - x^2} \) represents the upper half of a circle with radius 2 centered at the origin (0,0). The second curve \( x^2 + y^2 - 4x = 0 \) can be rewritten as \( (x - 2)^2 + y^2 = 4 \), which represents a circle with radius 2 centered at (2,0).

### Step 2: Find the intersection points
To find the area between these curves, we first need to determine where they intersect. We set the equations equal to each other:

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