Calculus MTH 250 Lecture 21 Previous Lectures Summary

$Previous Lecture’s Summary • Trigonometric integrals • Trigonometric substitutions • Partial fractions$

Today’s Lecture • Recalls • Improper integrals • Introduction to vectors • Dot product

Recalls We use the following identities to evaluate special of trigonometric integrals. Integral Identity

$Recalls How to find partial fractions: • Linear factors • Power of a linear$

Introduction to vectors Coordinate axes and planes. :

Introduction to vectors Distance formula in three dimensions: The distance │P 1 P 2│between

Lecture Summary • Recalls • Improper integrals • Introduction to vectors • Dot product

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Calculus (MTH 250) Lecture 21

$Previous Lecture’s Summary • Trigonometric integrals • Trigonometric substitutions • Partial fractions$

Previous Lecture’s Summary • Trigonometric integrals • Trigonometric substitutions • Partial fractions

Today’s Lecture • Recalls • Improper integrals • Introduction to vectors • Dot product of vectors • Cross product of vectors

Recalls

Recalls We use the following identities to evaluate special of trigonometric integrals. Integral Identity

Recalls

$Recalls How to find partial fractions: • Linear factors • Power of a linear$

Recalls How to find partial fractions: • Linear factors • Power of a linear factor • Quadratic factor, we break it down to partial fractions as follows:

Recalls

Improper integrals

Improper integrals Conti. . Therefore,

Improper integrals

Introduction to vectors Coordinate axes and planes. :

Introduction to vectors Distance formula in three dimensions: The distance │P 1 P 2│between the points P 1(x 1, y 1, z 1) and P 2(x 2, y 2, z 2) is

Introduction to vectors

Dot product of vectors

Cross product of vectors

Lecture Summary • Recalls • Improper integrals • Introduction to vectors • Dot product of vectors • Cross product of vectors