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Definite Integrals

Definite Integrals

Averages with Functions Exercises

Example 1

Let f (x) = 3x. Find a constant m such that

Example 2

Let f (x) = x. Find a constant m such that

Example 3

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  f (x) = x on [-10, 0]

Example 4

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  on [-2, 2]

Example 5

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  • f (x) = sin x on [-π, π]

Example 6

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  • f (x) = 3x + 2 on [1, 4]

Example 7

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  f (x) = -2x – 1 on [-4, 2]