FINDING AVERAGE inding Average Value of Function Over Interval Worksheet

Let f(x) be a function on the interval [a,b]. If we divided our interval into n equally sized intervals and took the sample at left endpoints f(x_i), then an approximation for the average value would be given by the formula:

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

Problem 1 :

f(x) = 2x² – 8x + 5; [0, 3]

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

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

Solution

Problem 5 :

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

Solution

Problem 6 :

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

Solution