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GeoGebraGeoGebra Classroom

Integrating even and odd functions

If a function has symmetry, say, if it's an even or odd function, then we can take advantage of that symmetry when integrating .
  • If is an even function, then it is symmetric across the -axis. We find
.
  • If is an odd function, then it is symmetric about the origin. We find
. In the figure, drag the blue control points to reshape the graph. Once the integral is displayed, you can drag the green point on the -axis to change the value of .