The Average Value of a Function G on 0 $\le$ X $\le$

question 2

Multiple Choice

The average value of a function g on 0 $\le$ x $\le$ 2 is a constant $\bar{g}$ given by $\bar{g}=\frac{1}{2-0} \int_{0}^{2} g(d) d x$ .Also, $\int_{0}^{2}(g(x) -\bar{g}) ^{2} d x \geq 0$ , since $(g(x) -\bar{g}) ^{2}$ is a square.Which of the following must be true?

• A) \(\left(\int_{0}^{2} g(x) d x\right)^{2} \leq \int_{0}^{2}(g(x))^{2} d x\)
• B) \(\left(\int_{0}^{2} g(x) d x\right)^{2} \geq \int_{0}^{2}(g(x))^{2} d x\)
• C) \(\left(\int_{0}^{2} g(x) d x\right)^{2}=\int_{0}^{2}(g(x))^{2} d x\)
• D)None of these

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