Question

The average value of the function f(x) = 2x - 2 over the interval [-3, 5] is given by the formula: f(c) = (1/(b-a)) * ∫[a to b] f(x) dx Where a = -3, b = 5, and f(x) = 2x - 2. Plugging these values into the formula gives: f(c) = (1/(5-(-3))) * ∫[-3 to 5] (2x - 2) dx Solving the integral gives: f(c) = (1/8) * [x^2 - 2x] from -3 to 5 f(c) = (1/8) * [(5^2 - 2*5) - ((-3)^2 - 2*(-3))] f(c) = (1/8) * [25 - 10 - 9 + 6] f(c) = (1/8) * 12 f(c) = 1.5 Therefore, the average value of the function f(x) = 2x - 2 over the interval [-3, 5] is 1.5.

          The average value of the function f(x) = 2x - 2 over the interval [-3, 5] is given by the formula:

f(c) = (1/(b-a)) * ∫[a to b] f(x) dx

Where a = -3, b = 5, and f(x) = 2x - 2. Plugging these values into the formula gives:

f(c) = (1/(5-(-3))) * ∫[-3 to 5] (2x - 2) dx

Solving the integral gives:

f(c) = (1/8) * [x^2 - 2x] from -3 to 5
f(c) = (1/8) * [(5^2 - 2*5) - ((-3)^2 - 2*(-3))]
f(c) = (1/8) * [25 - 10 - 9 + 6]
f(c) = (1/8) * 12
f(c) = 1.5

Therefore, the average value of the function f(x) = 2x - 2 over the interval [-3, 5] is 1.5.
        
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Added by Denise V.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The average value of the function f(x) = 2x - 2 over the interval [-3, 5] is given by the formula: f(c) = (1/(b-a)) * ∫[a to b] f(x) dx Where a = -3, b = 5, and f(x) = 2x - 2. Plugging these values into the formula gives: f(c) = (1/(5-(-3))) * ∫[-3 to 5] (2x - 2) dx Solving the integral gives: f(c) = (1/8) * [x^2 - 2x] from -3 to 5 f(c) = (1/8) * [(5^2 - 2*5) - ((-3)^2 - 2*(-3))] f(c) = (1/8) * [25 - 10 - 9 + 6] f(c) = (1/8) * 12 f(c) = 1.5 Therefore, the average value of the function f(x) = 2x - 2 over the interval [-3, 5] is 1.5.
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Transcript

-
00:01 Hello, welcome to this lesson.
00:02 In this lesson we have been given the average value of f of x is c and we find the average value of negative f of x.
00:11 So the average value of f of x is given as 1 on b minus a integral a to b of f of x dx.
00:25 So this is supposed to be the c and here we can conclude that we have f of x which is equal to 1 on b minus a times b minus a okay times c.
00:57 So if we have negative f of x, we would have the integral b minus a 1 on b minus a integral from a to b...
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