6.5 Average Value of a Function/17

1. Use the Average Value from a to b:

$f_{\text{avg}}={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx{\frac {1}{12}}\int _{0}^{12}50+14\sin({\frac {\pi }{12}}t)\,dt={\frac {1}{12}}[50t-<math>{\begin{aligned}u&={\frac {\pi }{12}}\end{aligned}}$

${\begin{aligned}u=ln(p)\quad \quad dv=p^{5}dp\\[2ex]du={\frac {1}{p}}\quad \quad \quad v={\frac {1}{6}}p^{6}\\[2ex]\end{aligned}}$