1. **State the problem:** Calculate the definite integral $$\int_1^6 x \, dx$$. 2. **Formula and rules:** The integral of $$x$$ with respect to $$x$$ is given by $$\int x \, dx = \frac{x^2}{2} + C$$, where $$C$$ is the constant of integration. 3. **Evaluate the definite integral:** Use the Fundamental Theorem of Calculus: $$\int_1^6 x \, dx = \left[ \frac{x^2}{2} \right]_1^6 = \frac{6^2}{2} - \frac{1^2}{2}$$ 4. **Calculate the values:** $$\frac{6^2}{2} - \frac{1^2}{2} = \frac{36}{2} - \frac{1}{2} = 18 - 0.5 = 17.5$$ 5. **Final answer:** $$\int_1^6 x \, dx = 17.5$$