MHB Integration by parts with absolute function

[Mathboi1]

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

 

[MarkFL]

Using a CAS, I get:

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

 

[Mathboi1]

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?

 

[Greg]

Factor $p$ out of the integrand.