How do you find the average value of #f(x)=-2x^3+10x^2-7x+5# as x varies between #[1/2,3]#?
1 Answer
Jan 8, 2017
Explanation:
f(x) is continuous on the closed interval
#[1/2,3]# The average value of f(x) is found using.
#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]=[1/2,3]#
#rArr1/(5/2)int_(1/2)^3(-2x^3+10x^2-7x+5)dx#
#=2/5[-1/2x^4+10/3x^3-7/2x^2+5x]_(1/2)^3#
#=2/5[(-81/2+90-63/2+15)-(-1/32+5/12-7/8+5/2)]#
#=2/5[33-193/96]=595/48#
