MAT 3751Analysis II

5.2

The Riemann Integral Part I

http://myhome.spu.edu/lauw

References

Bloch 5.2

Homework

Team HW Due Next Friday Again, do it ASAP

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 )(

Recall Calculus II

ith subinterval sample point

xxf i )(

Recall Definition

The Definite Integral of f from a to b

n

ii

n

b

axxfdxxf

1

)(lim)(

Partition, Norm, Representative Set, and Riemann Sum

Partition, Norm, Representative Set, and Riemann Sum

Example 1

Example 1

n

Example 2

Example 2

Example 2

Example 2

Riemann Integrals and Riemann Integrable

Riemann Integrals and Riemann Integrable

Lemma

Example 3