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Sigma Notations

Sigma Notations. This tells us to end with k=100. This tells us to add. This tells us to start with k=1. Example. Formula. Sigma Notations. Formula. Example. Riemann Sum. is called a partition of [ a , b ]. Example. Is a partition of [ 0 , 10 ].

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Sigma Notations

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  1. Sigma Notations This tells us to end with k=100 This tells us to add. This tells us to start with k=1 Example Formula

  2. Sigma Notations Formula Example

  3. Riemann Sum is called a partition of [a, b]. Example Is a partition of [0, 10]. Is a partition of [0, 9]. Is a partition of [0, 10].

  4. Riemann Sum subinterval widths Example Is a partition of [0, 10]. the largest of all the subinterval widths

  5. Riemann Sum Riemann sum for ƒ on the interval [a, b]. Example Find Riemann sum

  6. Riemann Sum Riemann sum for ƒ on the interval [a, b]. Example Find Riemann sum

  7. 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

  8. Riemann Sum Step 1 Step 2 Step 3

  9. Riemann Sum Riemann sum for ƒ on the interval [a, b]. Example Find Riemann sum partition the interval [0,1] into n equal subintervals

  10. Riemann Sum Riemann sum for ƒ on the interval [a, b]. Example Find Riemann sum partition the interval [0,1] into n equal subintervals

  11. The Definite Integral Definition: the definite integral of ƒ over [a, b] Example Find the definite integral of ƒ over [0, 1]

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

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

  14. The Definite Integral Remark:

  15. 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.

  16. 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.

  17. THE DEFINITE INTEGRAL Term-103

  18. THE DEFINITE INTEGRAL Property (1) Example:

  19. THE DEFINITE INTEGRAL Property (2)

  20. THE DEFINITE INTEGRAL Property (3)

  21. THE DEFINITE INTEGRAL Term-091

  22. The Definite Integral EXAM-1 TERM-102

  23. THE DEFINITE INTEGRAL Term-092

  24. THE DEFINITE INTEGRAL

  25. THE DEFINITE INTEGRAL Term-092

  26. THE DEFINITE INTEGRAL Term-082

  27. Term-092

  28. Term-082

  29. THE DEFINITE INTEGRAL Term-103

  30. DEFINITION

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