1. Implementing Technology into an Improper Integral Investigation Ryan Fox & Brian Gleason Doctoral Students University of Georgia Ryan Fox & Brian Gleason Doctoral Students University of Georgia

2. Goals for Today’s Presentation  Provide the motivation for the investigation  Present the examples from the investigation  Discuss the role of using technology in activity like this  Provide the motivation for the investigation  Present the examples from the investigation  Discuss the role of using technology in activity like this

3. The Original Investigation  Exercises that started the investigation (Anton, Bivens, & Davis 2002):  Notice a pattern?  Exercises that started the investigation (Anton, Bivens, & Davis 2002):  Notice a pattern?

4. The First Pattern  What the class came up with…  Starting to implement technology  Looking at the graphs. Graphing Calculator File.Graphing Calculator File  What happens if we choose a computer program that can manipulate symbols? Output from a Maple file. Output from a Maple file  What the class came up with…  Starting to implement technology  Looking at the graphs. Graphing Calculator File.Graphing Calculator File  What happens if we choose a computer program that can manipulate symbols? Output from a Maple file. Output from a Maple file

5. Extending the Pattern…  What about changing the lower limit of integration?  Here are some of the exercises we looked at.  What about changing the lower limit of integration?  Here are some of the exercises we looked at.

6. Quick Question  Did the previous exercises modify the conjecture?  What were those changes, if they were made?  Did the previous exercises modify the conjecture?  What were those changes, if they were made?

7. How does technology help with recognizing the patterns?  Looking at graphs. Graphing Calculator File #2.Graphing Calculator File #2  Looking at the output from Maple.output from Maple  Looking at graphs. Graphing Calculator File #2.Graphing Calculator File #2  Looking at the output from Maple.output from Maple

8. Extending the Pattern… (Part 2)  What happens when we change the value of the exponent? In particularly, what about when the value of the exponent is less than 1?  Here are some of the exercises we tackled…  What happens when we change the value of the exponent? In particularly, what about when the value of the exponent is less than 1?  Here are some of the exercises we tackled…

9. Where to go from here?  How far can computer software that manipulates symbols help us with calculations?  Can technology, like Maple, help to verify or prove what we have worked on?  How far can computer software that manipulates symbols help us with calculations?  Can technology, like Maple, help to verify or prove what we have worked on?

10. Thanks so much! See our websites by Googling our names (Ryan Fox & Brian Gleason) and “UGA”