What is the average value of the function #f(x)=e^4x^2# on the interval #[-1/4,1/4]#?
1 Answer
Apr 19, 2016
Explanation:
The average value of the function
#1/(b-a)int_a^bf(x)dx#
Thus here the average value is
#1/(1/4-(-1/4))int_(-1/4)^(1/4)e^4x^2dx=e^4/(1/2)int_(-1/4)^(1/4)x^2dx=2e^4[x^3/3]_(-1/4)^(1/4)#
#=2e^4[(1/4)^3/3-(-1/4)^3/3]=2e^4[1/192-(-1/192)]=e^4/48#
