1. Stating the problem: We need to evaluate the definite integral $$\int_3^6 x \, dx$$. 2. Find the antiderivative of the integrand. The antiderivative of $$x$$ is $$\frac{x^2}{2}$$. 3. Apply the Fundamental Theorem of Calculus to evaluate the definite integral: $$\int_3^6 x \, dx = \left[ \frac{x^2}{2} \right]_3^6 = \frac{6^2}{2} - \frac{3^2}{2}$$. 4. Calculate the values: $$\frac{6^2}{2} = \frac{36}{2} = 18$$ $$\frac{3^2}{2} = \frac{9}{2} = 4.5$$. 5. Subtract to find the final answer: $$18 - 4.5 = 13.5$$. Therefore, $$\int_3^6 x \, dx = 13.5$$.