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

1 Answer
Feb 17, 2016

Average value #= 22#

Explanation:

The average value of #y=3x^2-2x# over the interval #[2,4]#
is the area under the curve divided by the width of the interval.

The area under the curve for the interval #(2,4)# is
#color(white)("XXX")A=int_2^4(3x^2-2x) dx#

#color(white)("XXXx")=int_2^4(3x^2)dx - int_2^4(2x)dx#

#color(white)("XXXx")=x^3]_2^4 - x^2]_2^4#

#color(white)("XXXx")=(64-8) - (16-4)#

#color(white)("XXXx")=56-12 = 44#

The width of the interval #[2,4]# is #4-2=2#

So the average value of #y# over this interval is #44/2=22#