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Home Applications of the Integral Improper Integrals Closed Intervals
 
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Closed Intervals

THEOREM 1

If f is continuous on the closed interval [a, b] then the improper integral of f from a to b converges and equals the definite integral of f from a to b.

PROOF
We have shown in Section 4.2 on the Fundamental Theorem that the function

06_applications_of_the_integral-414.gif

is continuous on [a, b]. Therefore

06_applications_of_the_integral-415.gif

where 06_applications_of_the_integral-416.gif denotes the definite integral.
Home Applications of the Integral Improper Integrals Closed Intervals

Last Update: 2006-11-05