6.5 Average Value of a Function/5

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(t) = te^{-t^2} \quad [0, 5] }

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} f_{avg} &= \frac{1}{5}\int_{0}^{5}te^{-t^2}\,dx = \frac{1}{5}\int_{0}^{5}-\frac{1}{2}(e^u)\,du \\[2ex] &= \frac{1}{5}\int_{0}^{25}e^u(-\frac{1}{2}du) = \frac{1}{10}\int_{-25}^{0}e^u\,du \\[2ex] &= \frac{1}{10}e^u \bigg|_{-25}^{0} = \frac{1}{10}-\frac{1}{10}e^{-25} = \frac{1}{10}(1-e^{-25}) \\[2ex] \end{align} }

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=t^2 \\[2ex] & \frac{du}{dt}=2t \\[2ex] & du=-2t\cdot{dt} \\[2ex] & -\frac{1}{2}du=t\cdot{dt} \\[2ex] \end{align} }