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Why isn't the integral counted twice?

Attachment 25941

in the above example when it says that you can add the integral from -2 to -5 TO the integral from -2 to -3, would it not double count the area between -2 and -3?

similar to an intersection of sets when you have A union B you have to minus A intersect B to get the correct area. Why does that idea not pertain to integrals? Or does it?

Re: Why isn't the integral counted twice?

Ignore the middle term in the answer. The area from -5 to -3 is (the area from -5 to -2 ) - (area from -3 to -2). There is no ambiguity here.

Re: Why isn't the integral counted twice?

Quote:

Originally Posted by

**kingsolomonsgrave** Attachment 25941
in the above example when it says that you can add the integral from -2 to -5 TO the integral from -2 to -3, would it not double count the area between -2 and -3?

$\displaystyle \int_{ - 5}^{ - 2} {f} = \int_{ - 5}^{ - 3} {f} + \int_{ - 3}^{ - 2} {f} $