AP Calculus

Recommendations

Info

Special Focus: The Fundamental Theorem of Calculus Now, you will create three lists. The first list, L1, consists of X values from the graph screen. These will serve as inputs into Y1 and Y2. To create L1, follow these steps: 1. Select 5:seq( from the LIST-OPS menu, as shown in the screen shot below. 2. Fill in the arguments as shown below. 3. The STO> command is on the keypad, directly above the ON key. 4. To enter L1, type [2nd] 1. Now you will evaluate Y1 at each of the inputs in L1 and store the results in another list, L2. Select 1:Y1 from the VARS-YVARS(1:Function)menu, and enter L1 as the argument to Y1, as shown: Then evaluate Y2 at each of the inputs in L1, and store the results in list L3. Select 2:Y2 from the VARS-YVARS(1:Function)menu, and enter L1 as the argument to Y2, as shown: Be prepared to wait over a minute for all the integrals to be calculated. You will examine these values in a table format and use them in calculations later on. AP® Calculus: 2006–2007 Workshop Materials 63
Special Focus: The Fundamental Theorem of Calculus Each element of L3 results from the evaluation of a definite integral. For example, when 0.1, the second value of L1, is plugged into Y2, the value of ∫ ⎛ 2 ⎞ cos ⎜ ⎟ dT = 0. 09999975 ⎝ 2 ⎠ 0. 1 T 0 results, which is the second value in L3. 1. Explain why the first value in L3, which results from evaluating Y2(0), is 0. _______________________________________________________________ Look at the graph of the integrand, Y1(X). Use the graph to answer questions 2 and 3. 2. Why is the second value in L3 greater than 0? _______________________________________________________________ _______________________________________________________________ 0. 2 ⎛ 2 T ⎞ 3. Why is the third value in L3, which represents ∫ cos⎜ ⎟ dT , greater than 0 ⎝ 2 ⎠ 0. 1 ⎛ 2 T ⎞ the second value in L3, which represents ∫ cos⎜ ⎟ dT ? 0 ⎝ 2 ⎠ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ Select 1:EDIT on the STAT menu to see the table of inputs and outputs. Remember that ⎛ L1 contains the X-values; L2 contains the values of the integrand, cos T 2 ⎞ ⎜ ⎟ ; and ⎝ 2 L3 contains the values of the integral. ⎠ 64 AP® Calculus: 2006–2007 Workshop Materials
Page 1 and 2:
AP ® Calculus 2006-2007 Profession
Page 3 and 4:
The College Board: Connecting Stude
Page 5 and 6:
Table of Contents Stage Four: Confi
Page 7 and 8:
Special Focus: The Fundamental Theo
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16: Special Focus: The Fundamental Theo
Page 65: Special Focus: The Fundamental Theo
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Contact Us College Board Regional O
show all

AP Calculus

Create successful ePaper yourself

Delete template?

Save as template?