Question
Asked Jul 28, 2019
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Find the average value of the function f(x) = e-4x on the interval [0, 1/2 ]

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Expert Answer

Step 1

Given:

The function is f(x) = e−4x .

Definition used:

The average value of a function f(x) on the interval [a, b] is 

 

(1)
1
Avg ba
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(1) 1 Avg ba

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Step 2

Calculation:

From the given, the value of a and b is 0 and 1/2, respectively.

Compute the average value of the given function on [0,1/2] as follows.

Substitute a = 0 and b = 1/2 in equation (1).

1
-4x
1
.-0
2
avg
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1 -4x 1 .-0 2 avg

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Step 3

Let u = −4x, then du = −4dx and so...

-1
g2e'du
4
=-2e'du
4
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-1 g2e'du 4 =-2e'du 4

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Calculus

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