1. The problem asks to determine which option (A, B, or C) gives the best estimate of the area under the curve from $x=0$ to $x=12$ using vertical strips, and then to use that option to estimate the area. 2. Generally, the more strips used in a Riemann sum or area estimation, the better the approximation, because smaller strips capture the curve's shape more accurately. 3. Options A and B both use strips at every integer from 1 to 12 (12 strips), while option C uses strips at every odd integer from 1 to 11 (6 strips). 4. Since options A and B use more strips than C, they will give better estimates than C. 5. Without additional information about the difference between A and B (e.g., left endpoint, right endpoint, or midpoint sums), we assume both have the same number of strips and similar accuracy. 6. Therefore, either A or B gives the best estimate. We choose option A for the estimate. 7. To estimate the area using option A, sum the areas of the 12 strips. Each strip's area is approximately the function value at the strip times the width (which is 1). 8. Since the exact function values are not provided, we cannot compute a numeric estimate here. But the method is: $$\text{Area} \approx \sum_{i=1}^{12} f(x_i) \times \Delta x$$ where $\Delta x = 1$ and $x_i$ are the points at which the function is evaluated (e.g., left endpoints, right endpoints, or midpoints). Final answer: - a) Option A (or B) gives the best estimate because it uses more strips. - b) Use option A to estimate the area by summing the areas of the 12 strips. Since no numeric values are given, the exact numeric estimate cannot be computed here.