Reflection ;

- Write about your experience?

- what did you learn doing this project? - explain how each one (left, right, and trapezoidal approx.) worked

- What's your new knowledge?

- What are your thoughts after completion? (These are some sample questions that I came up with)

New ideas would be greatly appreciated! : if you have any questions please feel free to ask for clarification (:

Rectangular and Trapezoidal Approximations ime O 30 120 50 180 210 240 270 300 We recorded the velocity of the car at every 30 seconds (sec) along a road for 5 minutes. The car's odometer read that Velocity O 25 14 34 28 23 3 23 13 15 23 (mon) for those 5 mins, the car traveled 1.6 mil. We'll use the (mpn) 1(mph) FOT Left approx. 501 Right approx . left and right rectangular and Trapezoidal approximations 45 45 to determine which of the three is the most accurate . 40 40 a. left and Right approx. 35 35 Lio = ( f(0) + f ( 30)+ f ( 60) + f (90/ f(1201 + f ( 150) + f ( 180)+ f ( 210 ) + f (240 ) + f ( 270 ) 3 30 301 Lo = (0 + 25 + 14+ 34 + 28+ 23+ 31+ 23+ 13 + 15 ) 25 25 LID = 206 - 208= 3.4 mil 20 Rio = { f1301 + f(60) f ( 90)+ f( 1201+f(150) + f ( 180)+ f ( 210) + f(240)+ f ( Zolf ( 300 )3 15 157 R10 = ( 25 + 14 + 34 +28 + 23+ 31+ 23+ 13+ 15+ 23 ) 10 R10 = 229 -80 = 3.8 mi UT 30 60 90 10 120 150 180 210 240 270 300 50 180 210 240 270 300 b. Trapezoidal approx. [0, 300] n= 10 T ( sec ) T ( sec ) Summary Ax= b-a= 300-0 = 30 10 With the information and calculation we gathered, the left rectangular approximation Too = 32 2 f(01+ 2f ( 30) + 2f(60) + 2f ( 90) + 2f / 120 ) .... + 2 f/270) + f ( 300); gave us an estimation of 3. 4 mi and the right gave us a 3.8 mi. While the Tio= 32 ( 0 + 2 ( 25 ) + 2 ( 14 ) + 2 ( 34)+ 2 (28) + 2 ( 23 ) .... + 2 ( 15 ) + 233 trapezoidal gave us an estimation of 1. 8 mi. The estimate that was the most To = 32 (435) accurate in this case was the Trapezoid since according to the odometer, we travel Tio = 6525 - $600 = 1.8 mi 1. 6 mil . We think the way we could have made our estimates more accurate was least accurate . to change the math specifically for the rectangular because they were the