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

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

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?

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

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.

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?

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

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…

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?

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