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MAT 1234 Calculus I

MAT 1234 Calculus I. Section 3.9 Antiderivatives. http://myhome.spu.edu/lauw. Homework. WebAssign HW 3.9 Monday Quiz – 3.8, 3.9. Tomorrow. 9.4. Preview. Introduce antiderivatives Introduce the notations from section 4.4 (Indefinite integral). Reverse Operation of Differentiation.

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MAT 1234 Calculus I

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  1. MAT 1234Calculus I Section 3.9 Antiderivatives http://myhome.spu.edu/lauw

  2. Homework • WebAssign HW 3.9 • Monday Quiz – 3.8, 3.9

  3. Tomorrow • 9.4

  4. Preview • Introduce antiderivatives • Introduce the notations from section 4.4 (Indefinite integral)

  5. Reverse Operation of Differentiation f’(x)=g(x) g(x) is thederivative of f(x) f(x) is anantiderivative of g(x)

  6. Example 1 is the derivative of is an antiderivative of

  7. Example 1 is the derivative of functions of the form

  8. Q: Is it possible… is the derivative of functions of the form

  9. Consequence of the MVT a b

  10. Example 1 The most general antiderivative The antiderivative of is of the form Arbitrary constant

  11. Notation (Indefinite Integral) The notation always comes in pair.

  12. Notation If the independent variable is in u, then the differential is du

  13. Notation Always use parentheses if there is a sum/difference

  14. Formal Definition If then

  15. Formula where k is a constant Why?

  16. Formula Verify

  17. Example 2

  18. Formula (Linear Property) where k is a constant

  19. Example 3 Tradition

  20. Example 4

  21. Example 5

  22. Example 6

  23. Example 7

  24. Formula

  25. Example 8

  26. Example 9 If and , find .

  27. Caution

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