Part A Because you don't yet have an equation from your supervisor, choose one to help you set up the spreadsheet. Later, modify the spreadsheet when you receive the actual equation. Use spreadsheet software to: . Estimate the area that lies under the curvey = x + 1 between x = 0 and x = 10 Let the number of sub-intervals ben = 5 First calculate the area using left endpoints and then right endpoints Guidelines for Creating the Spreadsheet C: Insert a screen capture of your spreadsheet. BIUXX , 15px AA EE EEZ DVB Characters used: 0 / 15000 Part B Evaluate Jo (x +1) dx BIUXX , 15px 60 Characters used: 2 / 15000Part C Using the fact d1atjr= x + 'I is an increasing function, do your area estimates using the left and right endpoints make sense vten you compare them to the value of the integral ['3th + \"tint? Explain. ass: E:~.l"':EEV If you compare the estimate area from the left end point with the value of the integral, the estimate area ends up being less. By comparing the estimate area from the right end point with the value of the integral, the estimate area tends to be greater than the value. The value of the integral is 6:0, but left end point gave me a total area of 55 and the right gave me a total area of 65. Characters used: 391]! 15001] Part D lfx] were a decreasing function, which estimate [right or left]: would be an overestimate? Explain. are: ElitrIEEIv If x} were a decreasing function such as -x+1, the estimate area from the left end point tends to loe overestimated than the value of the integral. Characters used: 143! 15001] Part A 1. Copy the items in your spreadsheet from Step 1 and paste them elsewhere in the same spreadsheet page. 2. Use spreadsheet again to estimate the area that lies under the curvey = x + 1 between x = 0 and x = 10 this time letting the number of sub- intervals be n = 20. . First calculate the area using the left endpoints and then right endpoints. 3. Use spreadsheet software once more to: Estimate the area that lies under the curve y = x + 1 between 0 and 10 Let n = 20 . Calculate the area using midpoints. Insert a screen capture of your spreadsheet. BIUXX , 15px Characters used: 0 / 15000 Part B Are the results using the left and right endpoints closer to the value of the definite integral? Explain. BIUXX , 15px BVBV Characters used: 0 / 15000Part C When you created the midpoint portion of the spreadsheet, how did you do this? Why? BIUXX , 15px A Characters used: 0 / 15000Part A Your supervisor has finally given you the equation! It's y = 4 - Use your spreadsheet software and copy and paste the entire worksheet you previously completed. (Make sure you keep a copy of the items completed in Steps 1 and 2). Using the new copy, complete the following: 1. Use spreadsheet software and your previous setup to estimate the area below the curve for the equation y = zyg between 1 and 11 using the following criteria: . Left endpoints, n = 5 Right endpoints, n = 5 Left endpoints, n = 20 Right endpoints, n = 20 Midpoint, n = 20 2. Use your graphing calculator to see the graph of y = : + ; where 1 5 x = 11. 2.5 1.5 1.0 10 12 Insert a screen capture of the spreadsheet with data for the new equation. BIU X X2 15px Characters used: 0 / 15000 Part B Is this function increasing or decreasing? Based on this answer, can you determine whether there will be an underestimate or overestimate using the left endpoint? BIUXX , 15px v Characters used: 0 / 15000Part C Evaluate1 _#3 de . How does the value of the integral compare to your estimates? Explain. BIUXX , 15px Characters used: 0 / 15000 Part D If x is measured in yards and your boss wants a 2" thickness of mulch, how many cubic yards should he order? BIUXX , 15px BB v Characters used: 0 / 150001 . Start a blank spreadsheet (Excel, Googledocs, etc) Define a field in the spreadsheet where you're going to put the value for a; b, n and delta x. It's best to label these. You can start with something like this: 3. 4. Create a formula that will calculate x in cell B4. 5. 6. 10. 11. 12. 13. Fill in the values for a, b and n by placing the numbers in cells Bi, B2 and B3, respectively. Label cells Di and E1 as x sub i and ffx sub i), respectively. It should look like this: m x subi u sub I} Fill in the correct values for xi starting at cell D2. Remember. you're using the left endpoints but later you'll be using the right endpoints. (Note: If you'd like to reference the cell that contains x, simply type a dollar sign before the column letter and another dollar symbol before the row number. This will allow you to copy and paste the formula to other cells, but the formula will always use cell B4. Here's an example: $B$4} . Create a formula that will calculate fixi) in cell E2. (Note: lfyou'd like to reference the cell that contains Ax, simply type a dollar sign before the column letter and another dollar symbol before the row number. This will allow you to copy and paste the formula to other cells. but the formula will always use cell B4. Here's an example: $B$4] .Copythe formula in order to calculate the rest ofthe values for xi}. . Label cell F'l as "Area of rectangles from left". In cell F2. create a formula that will calculate the area ofa single strip or rectangle. Copy the formula to other cells in order to find the area of each rectangle. Sum the areas found in the previous step to get your estimated area using endpoints from the left. Label cell (31 as "Area of rectangles from right". In cell G2. create a formula that will calculate the area of a single strip or rectangle. Copy the formula to other cells in order to find the area of each rectangle. Sum the areas found in the previous step to get your estimated area using endpoints from the right