6.5 Average Value of a Function/2: Difference between revisions
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<math> | <math> | ||
f_{avg} = \frac{1}{\pi-(-\pi)}\int_{-\pi}^{\pi}\sin{(4x)}\,dx = \frac{1}{2\pi}\int_{-\pi}^{\pi}\sin{(4x)}\,dx | f_{avg} = \frac{1}{\pi-(-\pi)}\int_{-\pi}^{\pi}\sin{(4x)}\,dx = \frac{1}{2\pi}\int_{-\pi}^{\pi}\sin{(4x)}\,dx | ||
</math> | |||
<math> | |||
\begin{align} | |||
u &=4x \\[2ex] | |||
du &= 4dx \\[2ex] | |||
\frac{1}{4}du &= dx | |||
\end{align} | |||
</math> | </math> | ||
Revision as of 17:37, 7 September 2022
![{\displaystyle f(x)=\sin {(4x)}{\text{,}}\quad [-\pi ,\pi ]}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/0d26264e15aeb29ff049f70b6f38de6ed8709857)
![{\displaystyle {\begin{aligned}u&=4x\\[2ex]du&=4dx\\[2ex]{\frac {1}{4}}du&=dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/2d7068b9cc23779b7a691ebbcdd78a156d8eab11)