MAT 1235 Calculus II Section 7 7 Approximate

MAT 1235 Calculus II Section 7. 7 Approximate Integration http: //myhome. spu. edu/lauw

HW and … l l l No Web. Assign Do problem at the end of your HO. No need to turn in. HW template available here. It helps if you write out the details carefully with enough space to work with.

Idea l Many useful Integrals are difficult/impossible to evaluate by the Fundamental Theorem of Calculus

Probability & Statistics

Idea l In practice, we estimate the values of these integrals.

Method I: Riemann Sum

Method II: Trapezoidal Rule

Method III: Simpson’s Rule

Method III: Simpson’s Rule Even Number of Intervals

Facts l Why?

Facts l Why?

Rules l

Error Bounds - Trapezoidal Rule

Translation

Translation

Translation

Translation

Example 1 l

Example 1: Analysis l

Example 1: Analysis l

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Modified Closed Interval Method l

Modified Closed Interval Method l

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Calculations l

Example 1: Q: Can we choose a bigger K?

Remarks l We are solving for inequalities, not equations

Remarks l

Comparison…

Commercial l l Numerical Integration is part of the subject “Numerical Analysis”. If you are interest, we offer the class MAT 4725 every other year.

Remarks l