Question
State Bonnet's mean value theorem for integrals. Apply it to show that:
Answer :
Word Count : 274
The Mean Value Theorem for Integrals states that if \( f(x) \) is continuous on the interval \( [a, b] \), then there exists a point \( c \in [a, b] \) such that: \[ \int_{a}^{b} f(x) \, dx = f(c) \cdot (b - a) ______ _____ ______ ______ ________ _________ ________.
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The Mean Value Theorem for Integrals states that if \( f(x) \) is continuous on the interval \( [a, b] \), then there exists a point \( c \in [a, b] \) such that: \[ \int_{a}^{b} f(x) \, dx = f(c) \cdot (b - a) ______ _____ ______ ______ ________ _________ ________.
________ _______ ___ ____ ___ ______ ______.
_________ ___ ______ ___ __________ _________ ________ ________ ____.
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