mat 3751 analysis ii 5.2 the riemann integral part i
TRANSCRIPT
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MAT 3751Analysis II
5.2
The Riemann Integral Part I
http://myhome.spu.edu/lauw
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References
Bloch 5.2
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Homework
Team HW Due Next Friday Again, do it ASAP
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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
b ax
n
The area of the ith rectangle is
xxf i )(
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Recall Calculus II
ith subinterval sample point
xxf i )(
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Recall Definition
The Definite Integral of f from a to b
n
ii
n
b
axxfdxxf
1
)(lim)(
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Partition, Norm, Representative Set, and Riemann Sum
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Partition, Norm, Representative Set, and Riemann Sum
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Example 1
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Example 1
n
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Example 2
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Example 2
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Example 2
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Example 2
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Riemann Integrals and Riemann Integrable
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Riemann Integrals and Riemann Integrable
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Lemma
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Example 3