Integration by parts with absolute function

Click For Summary

Discussion Overview

The discussion revolves around the integration by parts involving an absolute function, specifically focusing on calculating the average value of a function between specified limits. Participants are exploring methods to solve for a variable denoted as P, with some expressing difficulties due to the absolute value of the cosine function.

Discussion Character

  • Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant, Mathsboi, presents a problem involving the average value of a function and expresses difficulty in solving it due to the absolute value of the cosine function.
  • Another participant provides a numerical approximation for P using a computer algebra system (CAS), stating that $$p\approx\frac{17812}{13715}$$.
  • A follow-up request for clarification on the method used to obtain the value of P is made, along with a query about finding P with different left-hand side values.
  • Another participant suggests factoring P out of the integrand as a potential approach to simplify the problem.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints and approaches to solving the problem, with no consensus reached on a single method or solution.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in the integration, and there are dependencies on specific values and definitions that remain unclear.

Mathboi1
Messages
2
Reaction score
0
Hi all,

I have the average value of a function between limits of 7.3826 and 0 which equals 0.4453. I have used the formula for average value function and attached the equation I need solving as I don't know how to use the Latex commands. P is what I am trying to work out. Unfortunately I have been unsuccessful since the absolute of cos makes this difficult. If anyone can solve this with working solution I'd be very grateful as I've spent all day trying to solve it.

View attachment 5087

Cheers,

Mathsboi
 

Attachments

  • power equation.png
    power equation.png
    1.5 KB · Views: 121
Physics news on Phys.org
Using a CAS, I get:

$$p\approx\frac{17812}{13715}$$
 
MarkFL said:
Using a CAS, I get:

$$p\approx\frac{17812}{13715}$$

Thanks for responding,

Can you please explain how you got here? I need to find p with different values of the LHS value and 0.125, keeping everything else the same. Is there a general formula I could use or can you show me steps to your solution?
 
Last edited:
Factor $p$ out of the integrand.
 

Similar threads

Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
3K
High School Why don't we account for the constant in integration by parts?
  • · Replies 16 ·
Replies
16
Views
4K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
2K
Graduate Memory issues in numerical integration of oscillatory function
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
MHB Visualization of Integration by Parts
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
1K
High School Integral of cosecant function: understanding different approaches
  • · Replies 14 ·
Replies
14
Views
4K
High School Are there mathematicians that dislike integral calculus?
  • · Replies 15 ·
Replies
15
Views
5K
High School Are Both Answers Correct for Trigonometric Substitution Integral?
  • · Replies 5 ·
Replies
5
Views
2K