(MTH 250) Lecture 21 Calculus. Previous Lecture’s Summary Trigonometric integrals Trigonometric substitutions Partial fractions.

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Presentation transcript:

(MTH 250) Lecture 21 Calculus

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. IntegralIdentity Recalls

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

Recalls

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

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