How do you find the average value of #f(x)=-x^4+2x^2+4# as x varies between #[-2,1]#?
1 Answer
Dec 6, 2016
Explanation:
Since f(x) is continuous on the closed interval [-2 ,1] the average value is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(1/(b-a)int_a^bf(x)dx)color(white)(2/2)|)))#
where [a ,b] is the closed interval.
#rArr1/(1+2)int_-2^1(-x^4+2x^2+4)dx#
#=1/3[-1/5x^5+2/3x^3+4x]_-2^1#
#1/3[(-1/5+2/3+4)-(-32/5-16/3-8)]#
#=1/3[67/15-(-296/15)]=1/3(363/15)=121/15#
