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5.2b The Definite Integral

- 4 Interpret definite integrals as AREAS
- The Midpoint Rule
- 5 Using the midpoint rule to compute ln2
- Properties of the definite integral
- 6 Use properties of integrals and formulas for

sums of powers. - 7 Illustrate properties of the integral.
- 8 Bound an integral.

5.2 5 Midpoint Sum

5.2 Algebraic Properties of the Integral

5.2 Comparison Properties of the Integral

5.3a Mean Value Theorem

THEOREM. If the function f is continuous on

a, b, then

5.3a Mean Value Theorem

PROOF. By the Heine-Borel Theorem, f has a

minimum m and a maximum M on a, b. Then

for every x in a, b

But by the intermediate value theorem, f takes on

every value between m and M on a,b. That means

that

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