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 $f$ on [20, 50].

${\begin{aligned}f_{avg}&={\frac {1}{30}}\int _{20}^{50}f(x)dx\\[2ex]&={\frac {1}{30}}\left[10{\bigg (}f(25)+f(35)+f(45){\bigg )}\right]={\frac {1}{3}}{\bigg (}38+29+48{\bigg )}\\[2ex]&={\frac {115}{3}}\\[2ex]&=38{\frac {1}{3}}\end{aligned}}$