Question

What is the average value of the function `f(x)=3x^2-4` on the interval [ 2, 6]?

Find the average value of the function `f(x)=3x^2-4` on the interval [ 2, 6]

Answer 1

`f_(avr)=48`

Explanation:

Remember, the average value of a function is given by

`color(blue)(f_(avr)=1/(b-a)int_a^bf(x)dx`

For your problem

`f_(avr)=1/(6-2)int_2^6 3x^2-4dx`

`color(white)(f_(avr))=1/4int_2^6 3x^2-4dx`

Integrate by the power rule

`f_(avr)=1/4[(x^3-4x)]_2^6`

`color(white)(f_(avr))=1/4((6^3-4*6)-(2^3-4*2))`

`color(white)(f_(avr))=1/4*192`

`color(white)(f_(avr))=48`