MEAN VALUE THEOREM FOR INTEGRALS WORKSHEET

For each problem, find the values of c that satisfy the Mean Value Theorem for Integrals.

Problem 1 :

f(x) = -x22+x+32 ; [-3,1]
mean-value-theorem-of-integral-q1

Solution

Problem 2 :

f(x) = 4/x2 ; [-4, -2]

Solution

For each problem, find the average value of the function over the given interval. Then, find the values of c that satisfy the Mean Value Theorem for Integrals.

Problem 3 :

f(x) = −x + 2; [−2, 2]

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Answer Key

1) average value = -2/3, c = (3 - 4√3)/3

2)  Average value = 1/2, c = -2√2

3)  Average value = 2, c = 0

4)  Average value = -4, c = 3.8

5) Average value = 1/6, c = -√6-3

6) Average value = -2, c = -3 and -5.

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