Integration by parts with absolute function

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SUMMARY

The discussion focuses on calculating the average value of a function using integration by parts, specifically addressing the challenges posed by the absolute value of the cosine function. The average value between the limits of 0 and 7.3826 is established as 0.4453, with a computed value of p approximated to be 1.298. The user seeks clarification on the steps involved in deriving this result and requests a general formula for varying the left-hand side (LHS) value while maintaining other parameters constant.

PREREQUISITES
  • Understanding of integration by parts
  • Familiarity with average value of a function
  • Knowledge of absolute functions in calculus
  • Experience using Computer Algebra Systems (CAS)
NEXT STEPS
  • Study the application of integration by parts in calculus
  • Learn how to compute the average value of a function over an interval
  • Explore the properties of absolute functions in mathematical analysis
  • Investigate the use of Computer Algebra Systems (CAS) for solving integrals
USEFUL FOR

Students, educators, and professionals in mathematics or engineering who are working on calculus problems involving integration by parts and absolute functions.

Mathboi1
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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
 

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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.
 

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