# Question Solved1 AnswerThis is a question ask for proof. Could any expert do it step by step coz I really confused about “at least one point c”. Question 1. Show that if $$f$$ is continuous on a closed interval $$[a, b]$$, then there exists at least one point $$c$$ in $$[a, b]$$ such that $\int_{a}^{b} f(x) d x=f(c)(b-a) .$ (Hint: Use the Mean value theorem).

This is a question ask for proof. Could any expert do it step by step coz I really confused about “at least one point c”.

Transcribed Image Text: Question 1. Show that if $$f$$ is continuous on a closed interval $$[a, b]$$, then there exists at least one point $$c$$ in $$[a, b]$$ such that $\int_{a}^{b} f(x) d x=f(c)(b-a) .$ (Hint: Use the Mean value theorem).
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Transcribed Image Text: Question 1. Show that if $$f$$ is continuous on a closed interval $$[a, b]$$, then there exists at least one point $$c$$ in $$[a, b]$$ such that $\int_{a}^{b} f(x) d x=f(c)(b-a) .$ (Hint: Use the Mean value theorem).