What is the average value of the function y=3x^{2}-2x on

Haylee Bowen

Haylee Bowen

Answered question

2022-04-16

What is the average value of the function y=3x22x on the interval [2,4]?

Answer & Explanation

Colin Collins

Colin Collins

Beginner2022-04-17Added 10 answers

The average value of y=3x22x over the interval [2,4]
is the area under the curve divided by the width of the interval.
The area under the curve for the interval (2,4) is
A=24(3x22x)dx
=24(3x2)dx24(2x)dx
=x3|{2}4x2|24
=(64-8)-(16-4)
=56-12=44
The width of the interval [2,4] is 4-2=2
So the average value of y over this interval is 442=22

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