# What is the average value of the function #f(x)=3x^2-4# on the interval [ 2, 6]?

##
Find the average value of the function #f(x)=3x^2-4# on the interval [ 2, 6]

Find the average value of the function

##### 1 Answer

May 29, 2018

#### Explanation:

Remember, the average value of a function is given by

#color(blue)(f_(avr)=1/(b-a)int_a^bf(x)dx#

For your problem

#f_(avr)=1/(6-2)int_2^6 3x^2-4dx#

#color(white)(f_(avr))=1/4int_2^6 3x^2-4dx#

Integrate by the power rule

#f_(avr)=1/4[(x^3-4x)]_2^6#

#color(white)(f_(avr))=1/4((6^3-4*6)-(2^3-4*2))#

#color(white)(f_(avr))=1/4*192#

#color(white)(f_(avr))=48#