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MAT 1221 survey of Calculus

MAT 1221 survey of Calculus. Section 6.1 Antiderivatives and Indefinite Integrals. http://myhome.spu.edu/lauw. Expectation. Simplify your answers. For problem 2: Formally answer the question in full sentence Pay attention to the units. Preview.

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MAT 1221 survey of Calculus

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  1. MAT 1221survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals http://myhome.spu.edu/lauw

  2. Expectation • Simplify your answers. • For problem 2: • Formally answer the question in full sentence • Pay attention to the units

  3. Preview • Introduce antiderivatives/ indefinite integral • Introduce integration formulas • Initial Value Problems • Word Problems

  4. Reverse Operation of Differentiation is the derivative of is an antiderivative of

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

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

  7. Example 1 The antiderivative of is of the form

  8. Notation

  9. Notation Differential Integral Sign

  10. Notation Integrand Constant of Integration/ Arbitrary Constant

  11. Notation The notation always comes in pair.

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

  13. Formal Definition

  14. Formula where k is a constant Why?

  15. Formula Verify

  16. Example 2

  17. Formula where k is a constant

  18. Example 3 Tradition

  19. Example 4

  20. Remark on the integral notation Use parenthesis if there are two or more terms in a sum or difference. Good! BAD

  21. Example 5

  22. Example 6

  23. Example 7

  24. Caution

  25. Differential Equations and Initial Conditions

  26. Differential Equations and Initial Condition If and , find .

  27. Formula • The antiderivative of the derivative is the original function.

  28. Example 8 If and , find .

  29. Example 9 The area of a healing wound is decreasing at a rate given by where is the time, in days, and is in square centimeters. (a) Find if

  30. Example 9 (b) Find the area of the wound after 7 days. The area of the wound after 7 days is cm2

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