Developing the Improper Integral

This little exploration, to be done in a small group of students, to lead them into the topic of Improper Integrals.  They see if the area under a curve diverges or converges by substituting progressively larger values in the upper bound of the integral.  Then, as a last step, they generalize by writing the improper integral as a formal limit as b approaches infinity.

The kids use finite values in a definite integral, observe a pattern in those values, then write their idea formally.

Thanks to master teacher Peter Mili for suggesting I put in the formal last step.  Here is the link to the Word document format of the exploration.  It’s about 3 pages long.  ImproperIntegrals

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