What is the average value of the function f(x)=\frac{3}{x} on

Aileen Rogers

Aileen Rogers

Answered question

2022-04-16

What is the average value of the function f(x)=3x on the interval [1,2e]

Answer & Explanation

unduncjineei5r3

unduncjineei5r3

Beginner2022-04-17Added 19 answers

The average value can be given by:
1baabf(x)dx
In this question we can use:
12e112e3xdx
Evaluating the integrand we get:
12e1[3ln(x)]12e=32e1(ln(2e)ln(1))
We can now tidy this up a little, using the rules of logarithms to re write:
=32e1(ln2+lneln1)
=3ln2+12e1
We can leave it at this exact value or approximate the solution by calculator to be:
1.1449

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