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MAT 3751 Analysis II 5.2 The Riemann Integral Part I

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Presentation on theme: "MAT 3751 Analysis II 5.2 The Riemann Integral Part I"— Presentation transcript:

1 MAT 3751 Analysis II 5.2 The Riemann Integral Part I http://myhome.spu.edu/lauw

2 References Bloch 5.2

3 Homework Team HW Due Next Friday Again, do it ASAP

4 Recall Calculus II Suppose f is a continuous function defined on [a,b], we divide the interval [a,b] into n subintervals of equal width The area of the i th rectangle is

5 Recall Calculus II i th subinterval sample point

6 Recall Definition The Definite Integral of f from a to b

7 Partition, Norm, Representative Set, and Riemann Sum

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9 Example 1

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11 Example 2

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15 Riemann Integrals and Riemann Integrable

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17 Lemma

18 Example 3


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