calculus
posted by li .
Find the average value of the function
f(x)=8x^25x+6 , on the interval [3,5]. Find the value of xcoordinate at which the function assumes it's average value.
what is the average value = to ?
what is the x coordinate = to ?
Thanks

Let f(x)=8x^25x+6
The average value is the definite integral divided by the interval.
I=∫f(x)dx
=∫(8x^25x+6)dx
=[(8/3)x^3(5/2)x^2+6x] from 3 to 5
=700/3
Average value, a
= I/(53)
= 350/3
To find x where f(x)=a, solve for x in
f(x) = 8x^25x+6 = 350/3
However, out of the two solutions, x=3.42 and x=4.045, you will report the solution which is within the interval [3,5] and reject all solutions outside of the interval.