Find the average value of the function f ( x ) = 5 x 4 f ( x ) = 5 x 4 on the interval 1 ≤ x ≤ 5

Question

need for homework help please asap

 

Answer 1

The average value of a function y = f(x) on the interval [a,b] is defined by 1/(b-a)∫_{(from a to b)}f(x)dx.

 

So, if f(x) = 5x⁴, then the average value of the function on the interval [1,5] is:

 

     1/(5-1)∫_{(from 1 to 5)}5x⁴dx = (1/4)[5⁵ - 1⁵]

 

                                          = 781

Answer 2

If f(x)=5x4, f(x)=20x

1≤x≤5 only for integrate number, then x=1,2,3,4,and 5. 

f(x)=20*1; 20*2; 20*3; 20*4 and 20*5. 

f(x)=20, 40, 60, 80, 100. The average will be 60.

Good luck.

Peter