I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 6.1 : Average Function Value
1. Determine \({f_{{\rm{avg}}}}\) for \(f\left( x \right) = 8x - 3 + 5{{\bf{e}}^{2 - x}}\) on \(\left[ {0,2} \right]\).
Show SolutionThere really isn’t all that much to this problem other than use the formula given in the notes for this section.
\[{f_{{\rm{avg}}}} = \frac{1}{{2 - 0}}\int_{0}^{2}{{8x - 3 + 5{{\bf{e}}^{2 - x}}\,dx}} = \frac{1}{2}\left. {\left( {4{x^2} - 3x - 5{{\bf{e}}^{2 - x}}} \right)} \right|_0^2 = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{2}\left( {5 + 5{{\bf{e}}^2}} \right)}}\]Note that we are assuming your integration skills are pretty good at this point and won’t be showing many details of the actual integration process. This includes not showing substitutions such as the substitution needed for the third term (you did catch that correct?).