1. The problem is to evaluate the definite integral $$\int_1^8 x \, dx$$. 2. The formula for the integral of a power function is $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $n \neq -1$. 3. Here, $n=1$, so the integral becomes $$\int x \, dx = \frac{x^{2}}{2} + C$$. 4. To evaluate the definite integral from 1 to 8, we use the Fundamental Theorem of Calculus: $$\int_1^8 x \, dx = \left[ \frac{x^2}{2} \right]_1^8 = \frac{8^2}{2} - \frac{1^2}{2}$$. 5. Calculate the values: $$\frac{64}{2} - \frac{1}{2} = 32 - 0.5 = 31.5$$. 6. Therefore, the value of the definite integral is $$31.5$$.