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We want to find the average of f(x) over the interval [0,2] where f(x) is the function f(x) = 5x.

Using the formula for average value:

average = (1/(b-a)) * âˆ«[a,b] f(x) dx

In this case, a = 0 and b = 2, so the average value can be calculated as:

average = (1/(2-0)) * âˆ«[0,2] 5x dx

Simplifying the integral:

average = (1/2) * âˆ«[0,2] 5x dx

Now we can solve the integral:

average = (1/2) * [ (5/2) * x^2 ] evaluated from 0 to 2

average = (1/2) * ( (5/2) * 2^2 – (5/2) * 0^2 )

average = (1/2) * ( (5/2) * 4 – (5/2) * 0 )

average = (1/2) * ( (5/2) * 4 )

average = (1/2) * ( 10 )

average = 5

Therefore, the average value of f(x) over the interval [0,2] is 5.

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