Long description: Fig29page3

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A diagram illustrates the projections of a line integral over a curve on the x-z and y-z planes.

Alt text: A diagram illustrates the projections of a line integral over a curve on the x-z and y-z planes.

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  • The image displays a three-dimensional coordinate system with axes labeled for \(x\), \(y\), and \(z\).
  • A curved path, labeled 'curve \(C\)', is drawn in the three-dimensional space, suggesting a path of integration.
  • Three line integrals are indicated as projections of the line integral \(\int_C f(x, y) d s\) onto the coordinate planes.
  • The projection onto the x-z plane is labeled \(\int_C f(x, y) d x\).
  • The projection onto the y-z plane is labeled \(\int_C f(x, y) d y\).
  • The integral \(\int_C f(x, y) d s\) is depicted with a series of vertical rectangular strips stacked along the \(y\)-axis, implying the surface element corresponding to the line integral.

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