Why Does Integration Matter in Solving for the Average Value of a Function?

  • MHB
  • Thread starter nghijen
  • Start date
In summary, the average value of a function involves a definite integral over an interval and is calculated by dividing the integral of the function over the interval by the length of the interval. The given interval in this problem is assumed to be [0, u] and the solution involves solving the definite integral. However, the approach taken by the person in the conversation is unclear and does not consider the necessary steps for integration.
  • #1
nghijen
2
0
I have attempted to solve the question but I still do not understand. Can someone please help me?
IMG_5255.jpeg
 
Physics news on Phys.org
  • #2
average value of a function involves a definite integral over an interval ... from your shading, is the given interval $[0,u]$ ?
 
  • #3
skeeter said:
average value of a function involves a definite integral over an interval ... from your shading, is the given interval $[0,u]$ ?

I am assuming it is [0, u] !
 
  • #4
nghijen said:
I am assuming it is [0, u] !

$\displaystyle 0 = \dfrac{1}{u-0} \int_0^u x^2(5-x) \, dx$

work it ...
 
  • #5
I frankly can't understand what you think you are doing! Much of what you are doing is determining where f(x)= 0. Okay that is at x= 5, which you have, and x= 0, which you ignore, but that is irrelevant anyway! The average value of a function, f(x), over interval a to b is the integral of f, from a to b, divided by b- a. But you show no attempt at integration!

Oh, and $-5^2(5- 5)= 0$, not -25! That is why you got x= 5 as a solution to $-x^2(x- 5)= 0$!
 
Last edited:

Related to Why Does Integration Matter in Solving for the Average Value of a Function?

1. What is the best way to approach a difficult question?

The best way to approach a difficult question is to break it down into smaller, more manageable parts. Start by identifying the key concepts and keywords in the question and then research each one individually. You can also try discussing the question with others or seeking help from a teacher or tutor.

2. How can I improve my understanding of a question?

One way to improve your understanding of a question is to read it multiple times and make sure you understand all the components. You can also try rephrasing the question in your own words or creating an outline to organize your thoughts. Don't be afraid to ask for clarification if you are still struggling to understand.

3. What should I do if I am still struggling to understand a question?

If you are still struggling to understand a question, try approaching it from a different angle. Look for additional resources such as textbooks, articles, or online tutorials. You can also try discussing the question with classmates or seeking help from a teacher or tutor.

4. How can I avoid getting overwhelmed when trying to understand a question?

To avoid getting overwhelmed when trying to understand a question, try breaking it down into smaller, more manageable parts. Take breaks if needed and don't be afraid to ask for help. It can also be helpful to create a study schedule and set aside dedicated time to work on understanding the question.

5. What are some common mistakes people make when trying to understand a question?

One common mistake people make when trying to understand a question is not reading it carefully and missing important details. Another mistake is not asking for clarification when needed. It is also important to avoid making assumptions or jumping to conclusions without fully understanding the question.

Similar threads

Replies
46
Views
1K
  • Calculus
Replies
5
Views
2K
Replies
31
Views
1K
Replies
3
Views
1K
  • Calculus
Replies
1
Views
1K
Replies
16
Views
2K
  • Calculus
Replies
25
Views
1K
Replies
8
Views
1K
Back
Top