1. 2006 Fall MATH 100 Lecture 141 MATH 100 Class 20 Line Integral

2. 2006 Fall MATH 100 Lecture 142 MATH 100 Class 20 Line Integral

3. 2006 Fall MATH 100 Lecture 143 MATH 100 Class 20 Line Integral

4. 2006 Fall MATH 100 Lecture 144 MATH 100 Class 20 Line Integral

5. 2006 Fall MATH 100 Lecture 145 MATH 100 Class 20 Line Integral Remark: 1. Independence of parameterization all produce 1/3

6. 2006 Fall MATH 100 Lecture 146 MATH 100 Class 20 Line Integral 2. Reversal of orientation If we reverse the orientation of the line integral, the line integral is the negation of the original result. all produce -1/3

7. 2006 Fall MATH 100 Lecture 147 MATH 100 Class 20 Line Integral 3. let -C denote C with reverse orientation when line integral over piecewise smooth curve Figure 18.1.2

8. 2006 Fall MATH 100 Lecture 148 MATH 100 Class 20 Line Integral

9. 2006 Fall MATH 100 Lecture 149 MATH 100 Class 20 Line Integral

10. 2006 Fall MATH 100 Lecture 1410 MATH 100 Class 20 Line Integral

11. 2006 Fall MATH 100 Lecture 1411 Vector notation: let and MATH 100 Class 20 Line Integral

12. 2006 Fall MATH 100 Lecture 1412 For parametric expression of curve MATH 100 Class 20 Line Integral

13. 2006 Fall MATH 100 Lecture 1413 and MATH 100 Class 20 Line Integral

14. 2006 Fall MATH 100 Lecture 1414 MATH 100 Class 20 Line Integral

15. 2006 Fall MATH 100 Lecture 1415 What about varying force along a smooth curve? Figure 18.1.4 Let MATH 100 Class 20 Line Integral denote the curve and denote the force

16. 2006 Fall MATH 100 Lecture 1416 MATH 100 Class 20 Line Integral

17. 2006 Fall MATH 100 Lecture 1417 MATH 100 Class 20 Line Integral

18. 2006 Fall MATH 100 Lecture 1418 MATH 100 Class 20 Line Integral

19. 2006 Fall MATH 100 Lecture 1419 MATH 100 Class 20 Line Integral

20. 2006 Fall MATH 100 Lecture 1420 MATH 100 Class 20 Line Integral

21. 2006 Fall MATH 100 Lecture 1421 MATH 100 Class 20 Line Integral