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HAVING FUN WITH ANTI-DERIVATIVES

HAVING FUN WITH ANTI-DERIVATIVES. Actually, the first thing we are going to do is to demonstrate a neat formula, namely the statement: Here is why: let be an anti-derivative of . Then, by the FTC, version 2 (we called it a corol-lary !) .

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HAVING FUN WITH ANTI-DERIVATIVES

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  1. HAVING FUN WITHANTI-DERIVATIVES Actually, the first thing we are going to do is todemonstrate a neat formula, namely the statement: Here is why: let be an anti-derivative of . Then, by the FTC, version 2 (we called it a corol-lary !)

  2. (Don’t be upset by Sam and Sue, we will give them proper names later!) So Let’s give Sam and Sue their proper names, And re-write the formula above as

  3. (ready?) But now, by the chain rule and

  4. The moral of this story is: • When taking the derivative of an integral • Use the FTC (evaluate the integrand properly) • But don’t forget the chain rule ! Here is an example:

  5. Another example: Do a few more from the textbook.

  6. Anti-derivative is an ugly word ! Using the con-nection between anti-derivatives and integrals provided by the FTC we write or more conventionally for any one anti-derivative of and call it the indefinite integral of a much better name! Now we get a few bricks and some mortar. We start with the mortar (rules)

  7. (very few) Now the bricks (depends on your memory !)

  8. and from trigonometry Any more ?

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