Implementing Technology into an Improper Integral

Investigation

Implementing Technology into an Improper Integral

Investigation

Ryan Fox & Brian GleasonDoctoral Students

University of Georgia

Ryan Fox & Brian GleasonDoctoral Students

University of Georgia

Goals for Today’s Presentation

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 InvestigationThe 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?

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1x10

1

∞

∫ 1x5

dx1

∞

∫1x3

dx1

∞

∫ 1x

dx1

∞

∫

The First PatternThe First Pattern

What the class came up with… Starting to implement technology

Looking at the graphs. Graphing Calculator File.

What happens if we choose a computer program that can manipulate symbols? Output from a Maple file.

What the class came up with… Starting to implement technology

Looking at the graphs. Graphing Calculator File.

What happens if we choose a computer program that can manipulate symbols? Output from a Maple file.

Extending the Pattern… 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.

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1x7

dx3

∞

∫ 1x4

2.5

∞

∫ dx

1x5

dx2

∞

∫ 1x2

dx12

∞

∫

Quick QuestionQuick 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?

How does technology help with recognizing the

patterns? Looking at graphs.

Graphing Calculator File #2. Looking at the output from Maple.

Looking at graphs. Graphing Calculator File #2.

Looking at the output from Maple.

Extending the Pattern…(Part 2)

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…

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1x0.5

dx1

∞

∫ 1x0.2

dx1

∞

∫ 1x0.03

dx1

∞

∫

Where to go from here?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?

Thanks so much!Thanks so much!

See our websites by Googling our names (Ryan Fox & Brian

Gleason) and “UGA”

See our websites by Googling our names (Ryan Fox & Brian

Gleason) and “UGA”