FIND THE AVERAGE VALUE OF THE FUNCTION ON THE INTERVAL

For each problem, find the average value of the function over the given interval.

Problem 1 :

f(x) = 2x² – 8x + 5; [0, 3]

Solution :

a = 0, b = 3, then b - a = 3 - 0 ==> 3

So, the average value of the given function in the given interval is -1.

Problem 2 :

Solution :

a = 0, b = 1, then b - a = 1 - 0 ==> 1

So, the average value of the given function in the given interval is 3.34.

Problem 3 :

Solution :

a = 0, b = 1, then b - a = 1 - 0 ==> 1

So, the average value of the given function in the given interval is 4 ln 2.

Problem 4 :

f(x) = -x + 1; [-4, 0]

Solution :

a = -4, b = 0, then b - a = 0 + 4 ==> 4

So, the average value of the given function in the given interval is 3.

Problem 5 :

f(x) = 2x + 1; [-4, 0]

Solution :

a = -4, b = 0, then b - a = 0 + 4 ==> 4

So, the average value of the given function in the given interval is -3.

Problem 6 :

f(x) = 2x + 1; [-2, 3]

Solution :

a = -2, b = 3, then b - a = 3 + 2 ==> 5

So, the average value of the given function in the given interval is 2.