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Riemann Sum

Riemann Sum. Riemann Sum. Formula. Riemann Sum. Step 1. Step 2. Step 3. Riemann Sum. We start by subdividing the interval [a,b] into n subintervals. The width of the interval [a,b] is b-a. the width of each subinterval is. The subintervals are. Riemann Sum. Term-103.

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Riemann Sum

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  1. Riemann Sum

  2. Riemann Sum Formula

  3. Riemann Sum Step 1 Step 2 Step 3

  4. Riemann Sum We start by subdividing the interval [a,b] into n subintervals The width of the interval [a,b] is b-a the width of each subinterval is The subintervals are

  5. Riemann Sum Term-103

  6. Sec 5.3 The Definite Integral

  7. The Definite Integral Definition: the definite integral of ƒ over [a, b] Example: Find the definite integral of ƒ(x) = x + 2 over [ -1, 1 ] Definition: Remark: the definite integral of ƒ over [a, b]

  8. Partition is called a partition of [a, b]. Note that the length of subintervals are not the same Example Is a partition of [0, 10]. Is a partition of [0, 9]. Is a partition of [0, 10].

  9. Partition subinterval widths Example Def: Norm of the partition the largest of all the subinterval widths Is a partition of [0, 10]. Example

  10. Riemann Sum Riemann sum for ƒ on the interval [a, b]. Example: Find the Riemann sum for ƒ(x) = x + 2 over [ 0, 5 ]

  11. The Definite Integral Definition: the definite integral of ƒ over [a, b] Definition: the definite integral of ƒ over [a, b] Definition: the definite integral of ƒ over [a, b]

  12. The Definite Integral Notation: the definite integral of ƒ over [a, b] Remark: Remark:

  13. The Definite Integral Remark:

  14. The Definite Integral Example: Evaluate the following integrals by interpreting each in terms of areas.

  15. The Definite Integral Example: Evaluate the following integrals by interpreting each in terms of areas.

  16. The Definite Integral Area under the curve the definite integral of f from a to b If you are asked to find one of them choose the easiest one.

  17. Riemann sum for ƒ on the interval [a, b].

  18. Riemann sum for ƒ on the interval [a, b].

  19. The Definite Integral Example: Evaluate the following integrals by interpreting each in terms of areas. Example: Evaluate the following integrals by interpreting each in terms of areas.

  20. THE DEFINITE INTEGRAL Term-103

  21. THE DEFINITE INTEGRAL Property (1) Example:

  22. THE DEFINITE INTEGRAL Property (2)

  23. THE DEFINITE INTEGRAL Property (3)

  24. THE DEFINITE INTEGRAL Term-091

  25. THE DEFINITE INTEGRAL

  26. Average Value DEFINITION Example: Find the average value of the function over the interval [-2,2]

  27. Term-082

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