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Area under a function

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Consider a continuous, positive function f: R --> R. The graph of f(x) is the set of points in the (x,y) Cartesian plane such that y = f(x).

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Solution Summary

This provides several examples of working with area under given functions and the intermediate value theorem.

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Please see the attachment.

We kow that the area can be represented as a definite integral as follows.
.
(a) Since , , then for any , we have . Then we have
and
Thus ...

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