Thread: Average Value of a function

1. Average Value of a function

Can someone please explain how to find the average value of a function

Say I have f(x)=X^2+2 on [1,4]. I think I have to to 1/b-a, but that is about all I know to do.

2. 1/(a-b) * integral of F , bounds a to b. It's a simple concept really. You have the total area of a region. If you make a rectangle from a to b with the same area, but one height obviously, the way to find this height is to divide the area by the width.

3. Could you show me how to solve my example, because when I do it I do not get the correct answer which should be 9.

4. Originally Posted by gammaman
Can someone please explain how to find the average value of a function

Say I have f(x)=X^2+2 on [1,4]. I think I have to to 1/b-a, but that is about all I know to do.
$\displaystyle \frac{1}{3} * \int_{1}^{4}x^2+2x=[\frac{1}{3}*(x^3/3+2x)]_{1}^{4}$.

(64/3 +8)-(1/3 +2)=(88/3)-(7/3)=81/3=27. Now divide by 3 and we get 9.

5. Thank You for your help.

6. I would suggest using the THANKS button which is at the bottom right corner of every post. Click it to indicate a useful post.