{"id":170473,"date":"2024-03-08T21:15:27","date_gmt":"2024-03-08T21:15:27","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-to-find-average-value-on-a-closed-interval\/"},"modified":"2024-03-08T21:15:27","modified_gmt":"2024-03-08T21:15:27","slug":"how-to-find-average-value-on-a-closed-interval","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-average-value-on-a-closed-interval\/","title":{"rendered":"How to find average value on a closed interval?"},"content":{"rendered":"

Finding the average value of a function on a closed interval is a fundamental concept in calculus. The average value of a function f(x) on the interval [a, b] is given by the formula:<\/p>\n

Average value = 1\/(b-a) * integral from a to b of f(x)dx.<\/p>\n

To find the average value of a function on a closed interval, follow these steps:<\/p>\n

1. Calculate the integral of the function f(x) from a to b.
\n2. Subtract the value of the integral at point a from the value of the integral at point b.
\n3. Divide the result by the length of the interval (b-a).<\/p>\n

Let’s break down the steps with an example. Consider the function f(x) = x^2 on the interval [0, 2]. <\/p>\n

1. Calculate the integral of f(x) from 0 to 2:
\nintegral of f(x)dx = (1\/3)x^3 evaluated from 0 to 2 = (1\/3)(2)^3 – (1\/3)(0)^3 = 8\/3.<\/p>\n

2. Calculate the average value:
\nAverage value = (1\/(2-0)) * (8\/3) = 4\/3.<\/p>\n

Therefore, the average value of f(x) = x^2 on the interval [0, 2] is 4\/3.<\/p>\n

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