1. **Problem:** Evaluate the area between the graph of $f(x) = x$ and the x-axis on the interval $[0, 3]$. 2. **Formula:** The area under the curve from $a$ to $b$ is given by the definite integral: $$\text{Area} = \int_a^b f(x) \, dx$$ 3. **Step 1:** Write the integral for the given function and interval: $$\int_0^3 x \, dx$$ 4. **Step 2:** Find the antiderivative of $f(x) = x$: $$F(x) = \frac{x^2}{2}$$ 5. **Step 3:** Evaluate the definite integral using the Fundamental Theorem of Calculus: $$\int_0^3 x \, dx = F(3) - F(0) = \frac{3^2}{2} - \frac{0^2}{2} = \frac{9}{2} - 0 = \frac{9}{2}$$ 6. **Step 4:** Interpret the result: The area between the graph of $f(x) = x$ and the x-axis from $0$ to $3$ is $\frac{9}{2}$ square units. **Final answer:** $$\boxed{\frac{9}{2}}$$