Step 1 Spreadsheet:

0 i x sub i f (x sub i) Area of rectangles Area using trapezoids b= 10 0 0 n= 5 2 6 4 delta x= 2 4 5 10 8 6 7 14 12 Co 18 16 10 11 22 20 70 60Oi x sub i f( x sub i) c sub i f( c suk N b= 10 O O n= un 3 0.25 AN AX = N 5 0.75 UT 3 7 1.25 N 9 1.75 N 5 10 11 2.25 W 8 2.75 W 3.25 10 3.75 A 11 4.25 12 4.75 13 5.25 6 14 5.75 6 15 6.25 16 6.75 17 7.25 8 18 7.75 8 19 8.25 9 20 8.75 9 21 9.25 8 22 9.75 8 23 24 25 26 Area using left end points = SO 27 28 Area using right endpoints = 70 290i x sub i f( x sub i) c sub i f( c sub i) IN b= 10 0 0 3 n= 20 0.5 1.5 0.25 1.25 AX = 0.5 2 0.75 1.75 5 2.5 1.25 2.25 4 3 1.75 2.75 J 5 2.5 3.5 2.25 3.25 8 6 W 4 2.75 3.75 3.5 4.5 3.25 4.25 10 00 4 5 3.75 4.75 11 4.5 5.5 4.25 5.25 12 10 5 6 4.75 5.75 13 11 5.5 6.5 5.25 6.25 14 12 6 7 5.75 6.75 15 13 6.5 7.5 6.25 7.25 16 14 7 8 6.75 7.75 17 15 7.5 8.5 7.25 8.25 18 16 8 9 7.75 8.75 19 17 8.5 9.5 8.25 9.25 20 18 9 10 8.75 9.75 21 19 9.5 10.5 9.25 8.25 22 20 10 11 9.75 8.75 23 24 25 26 Area using left end points = 57.5 27 28 Area using right endpoints = 62.5 29 30 31 Area using midpoints 60 32 33Part A Your supervisor has nally given you the equation! It's yr 2 3%. 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 = \"I\": s 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 = 3% where 1 s x s 11. Characters used: 0 f 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? BIUX X 2 15px v Characters used: 0 / 15000 Part C Evaluate f 'da . How does the value of the integral compare to your estimates? Explain. BIUXX , 15 px v 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? BIU X X 2 15px AA EE EEEE V BBV Characters used: 0 / 15000