MHB Integration by parts with absolute function

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The discussion revolves around finding the value of P in an integration problem involving an absolute function, specifically the average value of a function between the limits of 0 and 7.3826, which is given as 0.4453. The user, Mathsboi, is struggling with the absolute value of cosine complicating the integration process and seeks assistance. A response using a Computer Algebra System (CAS) provides an approximate value for P as 17812/13715. Mathsboi requests clarification on the steps taken to reach this solution and inquires about applying different left-hand side values while maintaining consistency in other parameters. The conversation emphasizes the need for a clearer understanding of the integration process involving 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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