Line Integrals – Part 1 Line Integrals of Scalar Functions.

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Presentation transcript:

Line Integrals – Part 1 Line Integrals of Scalar Functions

The area of the curtain is approximately: The height of the kth panel is approximately

Line Integrals of Scalar Functions Approximate area: Taking the limit as n approaches infinity, gives the exact area:

Line Integrals of Scalar Functions Remarks:  The value of the line integral does not depend on the parameterization nor the orientation of the curve C, provided the curve is traversed once as t increases from a to b.

Line Integral of Scalar Functions – Example 1 =1 xy

Line Integrals of Scalar Functions  The value of the line integral does not depend on the parameterization of the curve C, provided the curve is traversed once as t increases from a to b.

Line Integrals of Scalar Functions – Example 2 a) Parameterize the line segment from A to B: b) The line segment from B to A can be parameterized as The answers to a) and b) are the same. Line integrals of scalar functions are independent of the orientation and parameterization of the curve. x yz z