Graphs that Intersect Multiple Times

These two functions intersect each other at about x = –2, x = 0 and about x = 2.3. The difference function for these two functions would have to be integrated in two separate parts.  One part would be from x = –2 to x = 0, the second from x = 0 to x = 2.3.  It would have to be integrated in two bits because one bit would be a positive area, and the other negative.  If it was done all in one go, these positive and negative areas would partially cancel each other out.

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Say we calculated the difference function this way:


We can plot the graph of this difference function:

Once the two areas A and B had been calculated, their absolute values would be taken.  Then to get the total area between the two functions, you could just add these two sub-areas. If you didn’t take their absolute values, the negative value of the B area would cancel against the positive value of the A area.