This calculus 2 video tutorial provides a basic introduction into the integral test for convergence and divergence of a series with improper integrals. To perform the integral test, let the sequence be equal to a function that is continuous, positive, and decreasing on the interval [1, infinity). If these conditions are met, then the infinite series will converge if the definite integral from 1 to infinity converges. If the integral test is divergent, then the series is divergent as well. Examples and practice problems include integration techniques such as u-substitution, power rule for integration, trigonometric substitution which leads to inverse tangent functions, and completing the square before integration. The divergent harmonic series is included in this video as well.

Improper Integrals:
https://www.youtube.com/watch?v=ND9cEdfCFr0

Converging & Diverging Sequences:
https://www.youtube.com/watch?v=XdkoTb8PEG0

Monotonic & Bounded Sequences:
https://www.youtube.com/watch?v=tHy3TXmZpF0

Absolute Value Theorem - Sequences:
https://www.youtube.com/watch?v=kH5Zqg5j-3M

Squeeze Theorem - Sequences:
https://www.youtube.com/watch?v=21loY9MBK3A

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Geometric Series & Sequences:
https://www.youtube.com/watch?v=zRKZ0-kOUZM

Introduction to Series - Convergence:
https://www.youtube.com/watch?v=zg9N2gAf6a4

Divergence Test For Series:
https://www.youtube.com/watch?v=nC_IU1IzzS4

Harmonic Series:
https://www.youtube.com/watch?v=OqBZCycIYfw

Telescoping Series:
https://www.youtube.com/watch?v=XVkdhU6nJbo

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Integral Test For Divergence:
https://www.youtube.com/watch?v=f9SJz4-UaQQ

Remainder Estimate - Integral Test:
https://www.youtube.com/watch?v=vaU5DDcTfZk

P-Series:
https://www.youtube.com/watch?v=x621rtIwb_4

Direct Comparison Test:
https://www.youtube.com/watch?v=oZtAgihok5s

Limit Comparison Test:
https://www.youtube.com/watch?v=LBxYQ0TJxYM

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https://www.video-tutor.net/

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https://www.patreon.com/MathScienceTutor/collections