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Integration by Substitution

Integration by Substitution. Lesson 5.5. Substitution with Indefinite Integration. This is the “backwards” version of the chain rule Recall … Then …. Substitution with Indefinite Integration. In general we look at the f (x) and “split” it into a g (u) and a du/dx So that ….

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Integration by Substitution

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  1. Integration by Substitution Lesson 5.5

  2. Substitution with Indefinite Integration • This is the “backwards” version of the chain rule • Recall … • Then …

  3. Substitution with Indefinite Integration • In general we look at the f(x) and “split” it • into a g(u) and a du/dx • So that …

  4. Substitution with Indefinite Integration • Note the parts of the integral from our example

  5. Example • Try this … • what is the g(u)? • what is the du/dx? • We have a problem … Where is the 4 which we need?

  6. Why is this now a 3? Where did the 1/3 come from? Example • We can use one of the properties of integrals • We will insert a factor of 4 inside and a factor of ¼ outside to balance the result

  7. Can You Tell? • Which one needs substitution for integration? • Go ahead and do the integration.

  8. Try Another …

  9. Assignment • Lesson 5.5 • Page 315 • Problems:1, 5, 7, 9, 15, 17, 21, 25, 31, 37, 41

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