Unit 8 Calc AB

[keen nexus]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[left token]

what have you done so far

do you know the average value of a function?

[urban owl]

To find the average value of e^(-x) over the interval [0, 2], we need to follow these steps:

1. Define the function: f(x) = e^(-x)
2. Define the interval: [0, 2]
3. Find the average value: (1/(2-0)) × ∫[0, 2] e^(-x) dx

Now, let's evaluate the integral:

∫[0, 2] e^(-x) dx = [-e^(-x)] [0, 2]
= -e^(-2) + e^0
= -e^(-2) + 1

Now, let's find the average value:

(1/2) × (-e^(-2) + 1)

Simplifying, we get:

0.5 - 0.5e^(-2)

So, the average value of e^(-x) over the interval [0, 2] is approximately 0.499665.

Note: The exact value is 0.5 - 0.5e^(-2), but 0.499665 is a close approximation.

[sand bolt]

Man, don’t give the answer away, you can give out the steps and ways to get the answer but don’t outright give it

[urban owl]

I'm extremely sorry for that, actually new here soo..

[sand bolt]

No it’s fine I understand, I’m just saying that it would be more helpful to not give the answer straight away, you don’t need to apologize

[urban owl]

Fine I will be more careful about that in future :))

[arctic star]

Thank you so much!

+close