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Chapter 5 – The Definite Integral

Chapter 5 – The Definite Integral. 5.1 Estimating with Finite Sums. Example Finding Distance Traveled when Velocity Varies. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x 2 from x= 0 to x= 3. p.270 (1-19, 26, 27). 5.2 Definite Integrals.

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Chapter 5 – The Definite Integral

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  1. Chapter 5 – The Definite Integral

  2. 5.1 Estimating with Finite Sums Example Finding Distance Traveled when Velocity Varies

  3. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x2 from x=0 to x=3

  4. p.270 (1-19, 26, 27)

  5. 5.2 Definite Integrals Sigma notation enables us to express a large sum in compact form: Ex) Ex) Ex) Ex)

  6. The Definite Integral as a Limit of Riemann Sums

  7. We have that Upper limit Integral sign Lower limit Variable of Integration Integrand

  8. Example Using the Notation Area Under a Curve

  9. Notes about Area The Integral of a Constant

  10. Evaluate the following integrals:

  11. p.282 (1-27, 33-39) odd

  12. 5.3 Definite Integrals and Antiderivatives

  13. Ex: Show that the value of Average (Mean) Value

  14. The Mean Value Theorem for Definite Integrals

  15. Integral Formulas This is known as the indefinite integral. C is a constant.

  16. Evaluate:

  17. p. 290 (1 – 29) odd 19 – 29 note Do (31-35) After 5.4

  18. 5.4 Fundamental Theorem of Calculus The Fundamental Theorem of Calculus – Part 1

  19. Evaluate the following: Find

  20. Find Find a function y = f(x) with derivative That satisfies the condition f(3) = 5.

  21. The Fundamental Theorem of Calculus, Part 2

  22. How to Find Total Area Analytically Find the area of the region between the curve y = 4 – x2, [0, 3] and the x-axis. Look at page 301 example 8.

  23. p.302 (1-57) odd

  24. 5.5 Trapezoidal Rule

  25. The Trapezoidal Rule

  26. Use the trapezoidal rule with n = 4 to estimate . Compare with fnint. Ex: An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. What was the average temperature for the 12-hour period?

  27. Simpson’s Rule Ex: Use Simpson’s rule with n = 4 to approximate

  28. p.312 (1-18)

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