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# Can the result of a definite integral be negative?

Posted on 2011-03-07
Medium Priority
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If I am integrating a definite integral, sometimes it is possible to end up with a negative value - but I thought a definite integral was an area, so what happens if my result is negative?
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Question by:purplesoup
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Accepted Solution

akajohn earned 1000 total points
ID: 35055418

http://www.teacherschoice.com.au/Maths_Library/Calculus/area_under_a_curve.htm

As a summary areas under the x-axis are negative and above the x-axis are positive.

So integrating a function like y=x from -3 to 3 will yield zero because the negative areas exactly cancels the positive area.

Hope this hleps,

A>
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LVL 18

Expert Comment

ID: 35055954
the area below the X axis is counted as negative.  Also you have probably integrated from say 1 to 3 where 1 is at the bottom and 3 is at the top, well if you switch 1 to the top and 3 to the bottom, the integral comes out as -1 x the first integral.
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Assisted Solution

phoffric earned 1000 total points
ID: 35056274
You should find these EE questions of use:
http://rdsrc.us/CWGwJg

http://rdsrc.us/Ifx2A1

The area can even be zero:
http://rdsrc.us/ka98W8

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