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4.1 : Anti-derivatives

4.1 : Anti-derivatives. Greg Kelly, Hanford High School, Richland, Washington. Consider:. or. then:. Given:. find. First, a little review:. It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears.

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4.1 : Anti-derivatives

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  1. 4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington

  2. Consider: or then: Given: find First, a little review: It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.

  3. Given: and when , find the equation for . This is called an initial value problem. We need the initial values to find the constant. An equation containing a derivative is called a differential equation. It becomes an initial value problem when you are given the initial condition and asked to find the original equation. If we have some more information we can find C.

  4. 4.1 Antiderivatives and Indefinite Integration

  5. 4.1 Antiderivatives and Indefinite Integration

  6. 4.1 Antiderivatives and Indefinite Integration

  7. 4.1 Antiderivatives and Indefinite Integration

  8. 4.1 Antiderivatives and Indefinite Integration

  9. 4.1 Antiderivatives and Indefinite Integration

  10. 4.1 Antiderivatives and Indefinite Integration

  11. 4.1 Antiderivatives and Indefinite Integration

  12. 4.1 Antiderivatives and Indefinite Integration

  13. 4.1 Antiderivatives and Indefinite Integration

  14. 4.1 Antiderivatives and Indefinite Integration

  15. Front Cover #15? 4.1 Antiderivatives and Indefinite Integration

  16. 4.1 Antiderivatives and Indefinite Integration

  17. 4.1 Antiderivatives and Indefinite Integration

  18. 4.1 Antiderivatives and Indefinite Integration

  19. 4.1 Antiderivatives and Indefinite Integration

  20. 4.1 Antiderivatives and Indefinite Integration

  21. 4.1 Antiderivatives and Indefinite Integration

  22. Basic Integration Rules These two equations allow you to obtain integration formulas directly from differentiation formulas, as shown in the following summary.

  23. Basic Integration Rules cont’d

  24. 4.1 Antiderivatives and Indefinite Integration

  25. Practice Exercises OriginalRewriteIntegrateSimplify

  26. HW 4.1 Wed: pg. 255, 5-14 all, 15-47 odd,55-63 odd 73,77, 79 Thurs: MMM pg. 124-125 Fri: More practice problems (4.1) 4.1 Homework

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