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