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Define Improper Integral

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What exactly is an improper integral? Why is there a difference between improper and proper integrals?

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This solution defines improper integral and highlights the differences between improper and proper integrals.

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An integral is said to be improper if either the interval of integration is not finite or if the function that is being integrated is not bounded (not continuous) in the interval of integration.
Below are examples to illustrate.

1. Interval of integration not finite

∫ e^(-2x) dx (from x=0 to ...

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