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Section 1 Goals

After completing your work on this section, you should be able to:

  • Explain what the line integral of a vector field over a curve measures.
  • Determine the sign of a line integral of a vector field geometrically.
  • Calculate the exact value of a line integral of a vector field algebraically.
  • Recognize that a line integral of a vector field depends upon the orientation of a curve and adjust the sign of an integral accordingly when a parameterization gives the wrong orientation.
  • Recognize that a line integral of a vector field is independent of parameterization provided the orientation is correct.