1 / 27

Understanding Antiderivatives and Indefinite Integrals in Calculus

In this section, we delve into the concepts of antiderivatives and indefinite integrals, which are essential to calculus. We will explore reverse differentiation operations, introducing the concept that if ( f'(x) = g(x) ), then ( f(x) ) is an antiderivative of ( g(x) ). The notation for indefinite integrals will also be defined, and we will discuss the importance of arbitrary constants. Various examples and applications will clarify these ideas, demonstrating the linear properties of antiderivatives and providing practice opportunities for upcoming quizzes.

mahon
Télécharger la présentation

Understanding Antiderivatives and Indefinite Integrals in Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related