As an apprentice working for 1 plus 1 Landscaping, you’re learning the tricks of the trade. Your boss wants you to calculate the
area between the edge of a garden bed and the side of a house. Using the area, she can calculate the amount of mulch she will need for this job. The edge is defined by the equation y = x + 1. You will use a spreadsheet program to estimate the area under the curve y = x + 1 between x = 0 and x = 10. Let the number of subintervals be n = 5. Follow these steps to calculate the area using right endpoints: Start a blank spreadsheet in Excel, Google Docs, or another spreadsheet program. Define a field in the spreadsheet where you’re going to put the values for a, b, n, and delta x (Δx). It’s a good practice to label these cells. You can start with something like this: Refer to the problem description to fill in the values for a, b, and n by placing the numbers in cells B1, B2, and B3, respectively. Create a formula that will calculate Δx in cell B4. Label the cells D1 and E1 x sub i and f(x sub i), respectively: Starting at cell D2, fill in the correct values for xi by using the right endpoints. (Note: If you’d like to reference the cell that contains Δx, simply type a dollar sign before the column letter and another dollar sign before the row number, like this: $B$4. This will allow you to copy and paste the formula to other cells, but the formula will always use, for example, cell B4.) Create a formula that will calculate f(xi) in cell E2. (Note: If you’d like to reference the cell that contains Δx, simply type dollar signs before the column letter and the row number, like this: $B$4. This will allow you to copy and paste the formula to other cells, but the formula will always use, for example, cell B4.) Copy the formula to calculate the rest of the values for f(xi). Label cell F1 Area of rectangles. In cell F2, create a formula that will calculate the area of a single strip or rectangle. Copy the formula to other cells to find the area of each rectangle. Add the areas found in the previous step to get your estimated area in cell F7 by using endpoints from the right. Using your spreadsheet calculations, determine the estimated amount of area the mulch will need to cover. Enter your answer in the response box. Save and upload the spreadsheet you created to verify your answer. 1
