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Numerade Educator

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Problem 54 Easy Difficulty

Suppose $ f $ has absolute minimum value $ m $ and absolute maximum value $ M $. Between what two values must $ \displaystyle \int^2_0 f(x) \,dx $ lie? Which property of integrals allows you to make your conclusion?

Answer

Using property 8

$2 m \leq \int_{a}^{b} f(x) d x \leq 2 M$

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Video Transcript

okay. Using appropriate eight, we know that, um, Times two minus zero is less than or equal to into girl from A to B after Rex d ox, less than or equal to from terms to minus zero, which we can simplify as to, um, as less than or equal to and to go from a to B. Rex detox less than or equal to two AM