Wednesday, November 11, 2009

Integration by Substitution: In Stages

  1. Evaluate a derivative by the chain rule. Ask students what the antiderivative of the answer is. Students answer correctly

  2. Introduce intergration by substitution. Students flail in confusion.

  3. Give students handy tips! If you see a something in parentheses, especially if it is raised to a power, multiplied by something else, you should expect to use substitution. If you see a bunch of stuff multiplied together, expect to use substitution. Let u be the exponent on e. Let u be the denominator. Let u be something in parentheses raised to a power.

  4. Evaluate a derivative by the chain rule. Ask students what the antiderivative of the answer is. Students write down crazy shit involving u.