Problems: Geometric Approach to Line Integrals
1. Let F(x, y) = ex y i describe a force field. Show without computation that the work
integral along the line segment from (2, 0) to (2, 4) is 0.
Answer: Since the vector dr points in the j direction we have F · dr = 0. Therefore
A
F · dr = 0.
2. Let C be the curve g(x, y) =
x3 y
+
xy 3
A
Vg · dr.
= 5. Find
C
A
Answer: Since C is a level curve for G we know Vg · dr = 0. Therefore,
Vg · dr = 0.
C
MIT OpenCourseWare
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18.02SC Multivariable Calculus
Fall 2010
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