5.3: FTC Changed History
This activity is intended to supplement Calculus, Chapter 4, Lesson 6.
Problem 1 – Constant integrand
Suppose you have the function
For each value of
1. Use the Integrate command (HOME > F3:Calc > 2:Integrate) to complete the table.



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2. If
3. For every 1 unit that
4. If you were to graph the ordered pairs
Use the Stats/List Editor to enter the data in the table above into list1 and list2. Then plot the data.
5. What does your graph look like? Was this graph what you predicted in Question 4?
6. If you changed the integrand from 1.5 to 0.5, what would the graph of
Problem 2 – NonConstant Integrand
Suppose you have the function
7. Complete the table.



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8. If
9. Explain why, when
10. Is the graph of
Problem 3 – An Integrand That Changes Sign
In the previous exercises, the function was positive over the interval. This time you are going to examine a function which changes sign,



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11. At what value of
12. a. What are all the values of
b. What is true at these values of
13. a. What are all the values of
b. What is true of the integrand at these values of
14. a. What is the smallest value of the integral, and at what value of
b. What happens with the integrand at this value of
15. Is the connection between the location of the minimum value of
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