Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
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?).