How do you find the average value of #f(x)=-x^5+3x^3# as x varies between #[0,1]#?
1 Answer
Nov 25, 2016
Explanation:
The average value of the function
#1/(b-a)int_a^bf(x)dx#
Which here gives us the average value
#1/(1-0)int_0^1(-x^5+3x^3)dx#
Integrating term by term using
#=[-x^6/6+(3x^4)/4]_0^1#
The
#-1/6+3/4=7/12#