What is the average value of a function #y=6/x# on the interval #[1,e]#?
1 Answer
Jul 30, 2016
Explanation:
The average value of the function
#1/(b-a)int_a^bf(x)dx#
So, where the function is
#1/(e-1)int_1^e 6/xdx#
The
#=6/(e-1)int_1^e 1/xdx#
Note that since the derivative of
#=6/(e-1)[ln(x)]_1^e#
Now evaluating:
#=6/(e-1)[ln(e)-ln(1)]#
#=6/(e-1)(1-0)#
#=6/(e-1)#