1. (MTH 250) Lecture 21 Calculus

2. Previous Lecture’s Summary Trigonometric integrals Trigonometric substitutions Partial fractions

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

4. Recalls

5. Recalls

6. We use the following identities to evaluate special of trigonometric integrals. IntegralIdentity Recalls

7. Recalls

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

9. Recalls

10. Improper integrals

17. Conti.. Therefore,

18. Improper integrals

27. Introduction to vectors Coordinate axes and planes.:

28. 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

29. Introduction to vectors

35. Dot product of vectors

37. Cross product of vectors

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