1. **Problem Statement:** Evaluate the integral $$\int_0^{10} g(x) \, dx$$ by interpreting it in terms of areas under the graph of $$g(x)$$. 2. **Understanding the graph:** From $$x=0$$ to $$x=10$$, $$g(x)$$ is a straight line decreasing from $$y=20$$ at $$x=0$$ to $$y=0$$ at $$x=10$$. 3. **Formula for area under a line segment:** The area under the line from $$x=a$$ to $$x=b$$ is the area of the trapezoid formed by the points $$(a,0), (a,g(a)), (b,g(b)), (b,0)$$. 4. **Calculate the area:** Here, the trapezoid has bases $$g(0)=20$$ and $$g(10)=0$$, and height $$10-0=10$$. 5. **Area formula:** $$\text{Area} = \frac{(g(0) + g(10))}{2} \times (10 - 0) = \frac{(20 + 0)}{2} \times 10 = 10 \times 10 = 100$$ 6. **Interpretation:** Since the graph is above the x-axis in this interval, the integral equals the positive area. **Final answer:** $$\int_0^{10} g(x) \, dx = 100$$