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mathman

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mathman

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fresh_42

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Mean value theorem for integration: https://en.wikipedia.org/wiki/Mean_value_theorem#Mean_value_theorems_for_integration

It requires a continuous function ##f(x)##, so one probably has to have a look on the proof. But if ##f## is continuous, we have ##\int_0^1f(x)dx = f(\xi)\cdot (1-0)## with a mean value ##a<f(\xi)<b##.

The general version has two functions: ##g## continuous, and ##f## integrable, and says ##\int_0^1f(x)g(x)dx=g(\xi)\int_0^1f(x)dx##. Maybe one can find an appropriate ##g## and apply this general version.

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Math_QED

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