![]() These exist and are values of somewhere on the interval, by the Extreme Value Theorem. Let and be the minimum and maximum values of on the interval. ![]() This is intuitively correct, because if the function is ever non-zero, then it must be strictly positive in some region and then the area underthe graph should be also strictly positive. Intuitively this is saying that that area under the graph of a non-negative continuous function can only be zero if the function is everywherezero. ![]() The Mean Value Theorem for integrals of continuous functionsTo get to the mean value theorem for integrals of continuous functions, we first prove the following preliminary, but basic and intuitively clearresult: Next: Summary of the Mean Up: Internet Calculus II Previous: Internet Calculus II The Mean Value Theorem for integrals of continuous functions
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