6.5 Average Value of a Function/15

The table gives values of a continuous function. Use the Midpoint Rule to estimate the average value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle f } on Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle [20, 50] } .

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} f_{avg} &= \frac{1}{30} \int_{20}^{50} f(x)dx \\[2ex] &=\frac{1}{30} \left[10\bigg( f(25)+f(35)+f(45) \bigg) \right] = \frac{1}{3} \bigg(38+29+48 \bigg) \\[2ex] &= \frac{115}{3} \\[2ex] &= 38 \frac{1}{3} \end{align} }