Overview
Now that we have finished our study of techniques of integration, we take stock of everything we have learned, and summarize when to use which method, and what to do if none of our methods (seem to) work: In those cases, we can use a Table of Integrals or a Computer Algebra System (CAS) like WolframAlpha.com or Sage (on CoCalc.com) to help us.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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Given an indefinite integral, recognize whether it is best evaluated with a Substitution, Integration by Parts, Partial Fraction Decomposition, Trigonometric Substitution, Weierstrass Substitution, or neither, and justify your choice.
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Be proficient with asking Integral-Calculator.com or WolframAlpha to calculate derivatives and integrals.
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(Optional:) Be proficient with asking Sage (on CoCocalc.com) to calculate derivatives and integrals.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Given an indefinite integral, make an informed and justified choice for the best approach to calculate it.
To prepare for class
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Read subsection 5.5.2 in Active Calculus: Using an Integral Table.
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Watch the following video (by JDS1854) which shows some examples on how to use integral tables:
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Read subsection 5.5.3 in Active Calculus: Using Computer Algebra Systems.
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Watch the following video (by Math Easy Solutions) which gives some tips on how to use a Computer Algebra System for integration correctly, using https://www.integral-calculator.com/ as an example:
