Area as an Integral

Proposition (Area as an Integral) Suppose is continuous and on the closed interval Then the area under the curve on is given by

    More generally, if is a continuous function and is sometimes positive and sometimes negative, then

        
        
where is the sum of all areas of the region where and where is the sum of all areas of the region where   

Example (Area as an Integral) Determine the area between the graph of and the -axis that is bounded between the lines and

    Solution.

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Area As An Integral
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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