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

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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