6.5 Average Value of a Function/17

1. Use the Average Value from a to b:

$f_{\text{avg}}={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx$

${\frac {1}{12}}\int _{0}^{12}50+14\sin({\frac {\pi }{12}}t)\,dt={\frac {1}{12}}[50t-$

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} u &= \frac{\pi}{12}t \quad \quad \quad \quad \quad \int14\sin(u)\frac{12}{\pi}\,du \\ \quad dt\cdot\frac{du}{dt} &= dt \quad \quad \quad \quad 14\cdot\frac{12}{\pi}\int\sin(u)\,du \\ \frac{12}{\pi}du &= dt \end{align} }