1. **State the problem:** Calculate the definite integral $$\int_3^9 x \, dx$$. 2. **Recall the formula:** The integral of $$x$$ with respect to $$x$$ is $$\frac{x^2}{2} + C$$, where $$C$$ is the constant of integration. 3. **Apply the definite integral formula:** $$\int_a^b f(x) \, dx = F(b) - F(a)$$ where $$F(x)$$ is the antiderivative of $$f(x)$$. 4. **Find the antiderivative:** $$F(x) = \frac{x^2}{2}$$. 5. **Evaluate at the bounds:** $$F(9) - F(3) = \frac{9^2}{2} - \frac{3^2}{2} = \frac{81}{2} - \frac{9}{2}$$. 6. **Simplify:** $$\frac{81}{2} - \frac{9}{2} = \frac{81 - 9}{2} = \frac{72}{2}$$. 7. **Final answer:** $$\boxed{36}$$. This means the area under the curve $$y = x$$ from $$x=3$$ to $$x=9$$ is 36.