1. 9.8 Line integrals Integration of a function defined over an interval [a,b] Integration of a function defined along a curve C We will study Curve integral

2. Example 1: Evaluation of the Line Integral Evaluate.along the the quarter-circle C (4,0) (0,4) Basic Idea is to Convert the line integral to a difinite integral

3. Example 1: Evaluation of the Line Integral Evaluate.along the the quarter-circle C (4,0) (0,4) Steps 1)Find the parametric equations of C : 2) let 3) Replace

4. Example 1: Evaluation of the Line Integral Evaluate.along the the quarter-circle C (4,0) (0,4)

5. In Problem 5 and 6, evaluate On the indicated curve C HW Exercises 9.8

6. Notation. or

7. In Problems 7-10, evaluate On the given curve C between (-1,2) and (2,5) Exercises 9.8 (-1,2) (2,2) (2,5) 9) 10) HW (-1,2) (2,0) (2,5) (-1,0)

9. Curve defined by an explicit function Example 2/ pp489 (2,8) (-1,-1) Evaluate where C is given by

10. Example 1: Evaluation of the Line Integral Evaluate.along the the quarter-circle C (4,0) (0,4) The line integral along C with respect to (wrt) arclength

11. In Problem 5 and 6, evaluate On the indicated curve C HW Exercises 9.8

12. C is a curve Terminology C is SMOOTHC is piecewise smooth

13. C is a curve Terminology C is closed curve C simple closed curve Does not cross itself

14. Evaluate On the closed curve C shown in figure Example 4: Closed Curve

15. WORK PHY-101 The work done in moving an object from x=a to x=b by a force F(x), which varies in magnitude but not in direction, is given by Math-301 F(x,y) is a force field given by F(x,y)= p(x,y) i + Q(x,y) j C is a cuve traced by r(t) = f(t) i + g(t) j WORK done by F along C or

16. Groups and leaders