Question

Calc Help: High School

Answer 1

First, what do you think the domain of this function is?

Answer 2

I got 2pi, I took the integral from -8 to 8 of sqrt(64-x^2) and got 100.531 and then divided that by 16 to get the average and got 2pi.

Answer 3

Think: which set or sets of input (x-) values are acceptable, and which are not?

Answer 4

I agree with your domain: [-8,8]. How did you integrate \[y = \sqrt{64-x^2}?\]

Answer 5

But you said you integrated from -8 to +8, didn't you?

Answer 6

You did the right thing there. So I'm puzzled by your "Any positive number except x=8 in this case" in describing the domain of this function.

Answer 7

Your work is all correct except for your "Any positive number except x=8 in this case." I asked you for the domain, not "the terms."

The domain is the set [-8,8]. which leads to your dividing the area under the curve of the given function by 16.

Answer 8

Did you actually integrate? If so, using what method?

I noticed that Sqrt(64-x^2) yields a formula for a circle of radius 8. So, instead of integrating, you could simply find the area of half a circle of radius 8, which is what you have in 100.53 square units.

Answer 9

Yes, you're correct and are finished with this problem solution (unless you want to revise your definition of "domain" in this case).

Answer 10

I used a calculator, because it is allowed. I was given full permission to utilize my resources and I am. I do not need to revise my definition of the domain because I misread what you were asking me. Thank you very much for your help and have a good day.