Question

,

Answer 1

what is the question? @jennisicle

Answer 2

oh ok @jennisicle

Answer 3

If you were given a set of numbers and you wanted to find the average, you would just add them all up and divide by the quantity in the interval right?

It works the same way for integrals, which is just another way of adding up all the values from -3 to 7. We have to divide by the length of the interval from -3 to 7. Does that hint at anything for you in terms of this problem?

Answer 4

I kind of see what you're saying, but I'm still a little confused how to set it up :s

Answer 5

Would I have to divide something by 8?

Answer 6

Our integral represents the sum of all these values of f(x) along the interval [-3, 7]. So we just need to divide by the length of the interval [-3,7] to find the average value. Do you know how to find the length of this interval? [-3, 7]

\( \displaystyle \dfrac{1}{b-a} \int_{a}^{b} f(x) \ dx \)

Answer 7

1/(7+3) from -3 to 7 f(x)dx?

Answer 8

Yep, sorry that formula is the average value of the function. The length of the interval part was just b-a, or 7 - (-3) = 10. :)

Answer 9

What do I have to use the 8 for though?

Answer 10

is it 1/10 * 8?

Answer 11

\( \displaystyle \dfrac{1}{7 - (-3)} \color{blue}{ \int_{-3}^{7} f(x) \ dx} \)
Yes. That is your definite integral that was given. So we just replace it by 8. 1/10 * 8.

Answer 12

And that;s just the average value then? Cool ^^

Answer 13

Yep! To recap:
We were given the definite integral over the interval.
To find the average value, we divide by the length of the interval |7 - (-3)| = 10. So integral from -3 to 7 of f(x) dx / 10 = 8 / 10. :)

Answer 14

Okay, perfect :) thanks

Answer 15

You're welcome!