6.5 Average Value of a Function/17: Difference between revisions
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\begin{align} | \begin{align} | ||
u &= \frac{\pi}{12}t \\ | 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 dt\cdot\frac{du}{dt} &= dt \\ | ||
\frac{12}{\pi}du &= dt | \frac{12}{\pi}du &= dt | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 18:57, 29 November 2022
1. Use the Average Value from a to b:
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_{\text{avg}} = \frac{1}{b-a}\int_{a}^{b}f(x)\,dx }
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 \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 \\ \frac{12}{\pi}du &= dt \end{align} }