Question

Find the average value of f(x) = x^2 - x on the interval [-1, 2].

A) -1
B) 0
C) 1
D) 2

Answer 1

The average value of f(x) = x^2 - x on the interval [-1, 2] is 2/3.

Step-by-step explanation:

To find the average value of the function f(x) = x^2 - x on the interval [-1, 2], we need to find the definite integral of f(x) over the interval and then divide it by the width of the interval.

The definite integral of f(x) over the interval [-1, 2] is:

[x^3/3 - x^2/2] evaluated from -1 to 2.

Plugging in the upper and lower limits, we get:

[2^3/3 - 2^2/2] - [-1^3/3 - (-1^2/2)] = 8/3 - 2/2 + 1/3 + 1/2.

Simplifying, we get:

8/3 - 1 - 1/6 = 5/3 - 1 = 2/3.

Therefore, the average value of f(x) on the interval [-1, 2] is 2/3.