# Integral Limits of a function

1. Aug 3, 2012

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

2. Aug 3, 2012

### 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.

3. Aug 3, 2012

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!

4. Aug 4, 2012

### HallsofIvy

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

5. Aug 6, 2012