1. Estimating with Finite Sums

2. Quick Review
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3. Quick Review Solutions
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4. What you’ll learn about
Distance Traveled
Rectangular Approximation Method (RAM)
Volume of a Sphere
Cardiac Output
… and why
Learning about estimating with finite sums sets the
foundation for understanding integral calculus.
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5. Example Finding Distance Traveled when Velocity Varies
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6. Example Finding Distance Traveled when Velocity Varies
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7. LRAM, MRAM, and RRAM approximations to the area under the graph of y=x2 from x=0 to x=3
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8. Example Estimating Area Under the Graph of a Nonnegative Function
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9. 5.2
Definite Integrals

10. Quick Review
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11. Quick Review Solutions
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12. What you’ll learn about
Riemann Sums
The Definite Integral
Computing Definite Integrals on a Calculator
Integrability
… and why
The definite integral is the basis of integral calculus,
just as the derivative is the basis of differential
calculus.
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13. Sigma Notation
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14. The Definite Integral as a Limit of Riemann Sums
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15. The Existence of Definite Integrals
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16. The Definite Integral of a Continuous Function on [a,b]
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17. The Definite Integral
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18. Example Using the Notation
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19. Area Under a Curve (as a Definite Integral)
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20. Area
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21. The Integral of a Constant
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22. Example Using NINT
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23. Definite Integrals and Antiderivatives
5.3
Definite Integrals and Antiderivatives

24. Quick Review
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25. Quick Review Solutions
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26. What you’ll learn about
Properties of Definite Integrals
Average Value of a Function
Mean Value Theorem for Definite Integrals
Connecting Differential and Integral Calculus
… and why
Working with the properties of definite integrals helps
us to understand better the definite integral. Connecting
derivatives and definite integrals sets the stage for the
Fundamental Theorem of Calculus.
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27. Rules for Definite Integrals
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28. Example Using the Rules for Definite Integrals
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29. Example Using the Rules for Definite Integrals
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30. Example Using the Rules for Definite Integrals
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31. Average (Mean) Value
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32. Example Applying the Definition
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33. The Mean Value Theorem for Definite Integrals
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34. The Mean Value Theorem for Definite Integrals
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35. The Derivative of an Integral
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36. Quick Quiz Sections
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37. Quick Quiz Sections
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38. Quick Quiz Sections
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39. Quick Quiz Sections
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40. Quick Quiz Sections
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41. Quick Quiz Sections
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