6.5 Average Value of a Function/2: Difference between revisions
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New upper limit: <math>4\pi = 4(\pi)/math><br> | New upper limit: <math>4\pi = 4(\pi)</math><br> | ||
New lower limit: <math>-4\pi = 4(-\pi)</math> | New lower limit: <math>-4\pi = 4(-\pi)</math> | ||
Revision as of 17:41, 7 September 2022
![{\displaystyle f(x)=\sin {(4x)}{\text{,}}\quad [-\pi ,\pi ]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/0d26264e15aeb29ff049f70b6f38de6ed8709857)
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_{avg} = \frac{1}{\pi-(-\pi)}\int_{-\pi}^{\pi}\sin{(4x)}\,dx = \frac{1}{2\pi}\int_{-\pi}^{\pi}\sin{(4x)}\,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 \begin{align} u &=4x \\[2ex] du &= 4dx \\[2ex] \frac{1}{4}du &= dx \end{align} }
New upper limit: 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 4\pi = 4(\pi)}
New lower limit: 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 -4\pi = 4(-\pi)}