1. **State the problem:** Evaluate the definite integral $$\int_3^{10} x \, dx$$. 2. **Formula used:** 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:** $$\int_3^{10} x \, dx = \left[ \frac{x^2}{2} \right]_3^{10} = \frac{10^2}{2} - \frac{3^2}{2}$$ 4. **Calculate the values:** $$\frac{10^2}{2} = \frac{100}{2} = 50$$ $$\frac{3^2}{2} = \frac{9}{2} = 4.5$$ 5. **Subtract to find the result:** $$50 - 4.5 = 45.5$$ 6. **Final answer:** $$\int_3^{10} x \, dx = 45.5$$ This means the area under the curve $$y = x$$ from $$x=3$$ to $$x=10$$ is 45.5 square units.