What is the average value of the function #f(x) = 4 - x^2# on the interval #[-2,2]#?
1 Answer
May 21, 2016
Explanation:
For a continuous function on the closed interval [a ,b] the
#color(blue)"average value "# from x = a to x = b is
#color(red)(|bar(ul(color(white)(a/a)color(black)(1/(b-a) int_a^bf(x)dx)color(white)(a/a)|)))#
#rArr1/(2-(-2))int_-2^2(4-x^2)dx#
#=1/4[4x-x^3/3]_-2^2#
#=1/4[(8-8/3)-(-8+8/3)]=1/4(32/3)=8/3#
