What Does the Lower Limit in This Integral Represent?

[femiadeyemi]

Hi All,

I need your help, we we have an intergral like this

$∫^{T}_{max \in \{0, t\}}$ f(x) dx

what is the meaning of the lower limit in this integral? Thanks in advance

 

[Mute]

The function max(a,b) is equal to a if a > b, or b if b > a. What the lower limit of your integral means, then, is that you have a function

$$g(t) = \int_{\mbox{max}(0,t)}^T dx~f(x).$$

If t is less than zero, then the lower limit is zero. If t is greater than zero, then the lower limit is t.

 

[femiadeyemi]

Thank you @Mute, you are safer! I still have couple more questions though:

1. How can someone arrive at this type of integral?

2. Assuming the upper limit of the integral, T>>y, how can I implement that in my solution. In between can you please recommend a textbook/paper that I can use for this type of problem, I still have more of weird ones like this. Thanks!

The function max(a,b) is equal to a if a > b, or b if b > a. What the lower limit of your integral means, then, is that you have a function

$$g(t) = \int_{\mbox{max}(0,t)}^T dx~f(x).$$

If t is less than zero, then the lower limit is zero. If t is greater than zero, then the lower limit is t.

 

[HallsofIvy]

You were the one who posted it! Where did you find it?

 

[femiadeyemi]

You were the one who posted it! Where did you find it?

I found it in a paper but the problem is that I couldn't make a sense out of how the equation of such was arrived at, so I was thinking if I could see some other example in which such equation was used, it will help to understand what I'm currently working on