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

595/48

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