Question 1044441
This problem was already solved previously elsewhere.

The average value of F(x) over the closed interval {{{0 <= x <= ln4}}} 

is given by 

{{{(1/(ln4-0))*int((e^(2x)-e^x), dx, 0, ln4) = (1/ln4)int(e^x*(e^x-1), dx, 0, ln4)}}}

= {{{(1/ln4)int((e^x-1), de^x, 0, ln4)}}}

= {{{(1/ln4)*(e^(2x)/2 - e^x)[0]^ln4}}}

Now finish the evaluation....