1. **State the problem:** We need to find the area of the region bounded by the curve $y = \sqrt{4 - x^2}$ and the x-axis. 2. **Understand the curve:** The equation $y = \sqrt{4 - x^2}$ represents the upper half of a circle centered at the origin with radius 2 because the full circle equation is $x^2 + y^2 = 4$. 3. **Set up the integral:** The area under the curve from $x = -2$ to $x = 2$ (the circle's radius limits) is given by the integral $$\text{Area} = \int_{-2}^{2} \sqrt{4 - x^2} \, dx$$ 4. **Use the formula for the area of a semicircle:** Instead of integrating, we can use the known formula for the area of a circle $A = \pi r^2$. Since this is a semicircle, $$\text{Area} = \frac{1}{2} \pi (2)^2 = 2\pi$$ 5. **Answer:** The area of the region bounded by the curve and the x-axis is $2\pi$. **Final answer:** (c) $2\pi$