1. **Problem Statement:** Estimate the area under the curve on the interval $[1,4]$ using the left-endpoint approximation with 3 rectangles. 2. **Formula and Explanation:** The left-endpoint approximation for area under a curve divides the interval into $n$ equal subintervals and uses the function value at the left endpoint of each subinterval to form rectangles. The area approximation is: $$\text{Area} \approx \sum_{i=0}^{n-1} f(x_i) \Delta x$$ where $\Delta x = \frac{b-a}{n}$ and $x_i = a + i \Delta x$. 3. **Calculate $\Delta x$:** $$\Delta x = \frac{4-1}{3} = 1$$ 4. **Determine left endpoints:** $$x_0 = 1, \quad x_1 = 2, \quad x_2 = 3$$ 5. **Estimate function values at left endpoints:** Since the exact function is not given, we estimate $f(1)$, $f(2)$, and $f(3)$ from the graph. Assuming approximate values: - $f(1) \approx 6$ - $f(2) \approx 7$ - $f(3) \approx 5$ 6. **Calculate area approximation:** $$\text{Area} \approx (f(1) + f(2) + f(3)) \times \Delta x = (6 + 7 + 5) \times 1 = 18$$ 7. **Interpretation:** The estimated area under the curve from $x=1$ to $x=4$ using the left-endpoint method with 3 rectangles is approximately $18$ unit². **Final answer:** $$\boxed{18}$$