6.5 Average Value of a Function/2

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}f(x)=\sin {(4x)}{\text{,}}\quad [-\pi ,\pi ]f_{avg}&={\frac {1}{\pi -(-\pi )}}\int _{-\pi }^{\pi }\sin {(4x)}\,dx={\frac {1}{2\pi }}\int _{-\pi }^{\pi }\sin {(4x)}\,dx&={\frac {1}{2\pi }}\int _{-4\pi }^{4\pi }\sin {u}{\frac {1}{4}}\,du\end{aligned}}<math>{\begin{aligned}u&=4x\\[2ex]du&=4dx\\[2ex]{\frac {1}{4}}du&=dx\end{aligned}}}

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)}