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5.3 Properties of definite integrals

For definite integrals we can, using the fundamental theorem of calculus, determine quite a few properties.

  1. aaf(x)dx=0.
  2. abf(x)dx=baf(x)dx. The definite integral is not just an area!
  3. baf(x)dx=caf(x)dx+cbf(x)dx. The value of c is arbitrary, it doesn’t have to be between a and b!
  4. baf(x)dx0 if f(x)0.
  5. If mf(x)M and ba, then m(ba)≤∫baf(x)dxM(ba).