The Fundamental Theorem of Calculus

Practice in the mechanics of using substitution in integration is often hard to come by in enough quantity for learners to really wrap their heads around the nuances of the technique. This worksheet set with solution key and worked examples solves that problem, with dozens of definite and indefinite integrals for learning and practice. Multiple kinds of anti-derivatives are covered, from trigonometric to polynomial to rational with everything in between, and the differences between definite and indefinite integration are treated with care. A great worksheet set to stick in the teaching binder for integration practice days.

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CCSS: Adaptable
Instructional Ideas

  • Great remediation resource, with brief presentation and lots of problems for working and explaining
  • Have learners create their own presentations for assigned problems to explain to the class
  • Consider using as bellringers or other warm-up problems, keeping substitution and the differences between indefinite and definite integration front-and-center
Classroom Considerations

  • Answer keys on two of the three worksheets are not separated from the classwork, may require manipulation before copying
  • Space provided on worksheet is not enough for showing work on each problem
  • Main resource presentation matches two problems off of the additional resource sheet about indefinite integration, and two off of the sheet about definite integration
  • Presentation PDF would make an excellent interactive whiteboard lesson, with steps revealed as the problem is solved
Pros

  • Worked examples provide useful techniques for other problems
  • Many problems of both definite and indefinite type
  • Comprehensive solution key provided for each worksheet
Cons

  • No teaching notes or strategies provided
Common Core