SOLUTION: Find the average value of the function f(x)= x^5 (8x^2 - 12) over0 ≤ x ≤2.

Algebra ->  Linear-equations -> SOLUTION: Find the average value of the function f(x)= x^5 (8x^2 - 12) over0 ≤ x ≤2.      Log On


   

Question 1034671: Find the average value of the function f(x)= x^5 (8x^2 - 12) over0 ≤ x ≤2.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, for
f(x)= x^5 (8x^2 - 12) = 8x^7 - 12x^5
we integrate and then multiply by 1%2F%282-0%29
So we get
Integral of f(x) = x^8 - 2x^6
evaluated from 0 to 2 gives
256 - 128 = 128
Now multiply that by 1/2 and get the average value
64