Thread: Can someone explain this integral?

1. Can someone explain this integral?

Hi,
I have the following step in a derivation

$\displaystyle \lambda^2 \cdot \exp{(-\lambda w)} \int_{0}^{w} \mathrm{d} x = \lambda^2 \cdot w \cdot \exp{(-\lambda w)}$

where $\displaystyle w \geq 0$ and $\displaystyle x \geq 0$ and $\displaystyle w = x + y$

Whats going on here? Is the integral over w w.r.t. x w by definition? How can you have an integral over no function?

I guess this is pretty school-ish, but I haven't seen it before and would appreciate any clarity that can be provided.

Thanks, MD

2. Re: Can someone explain this integral?

The integral is just $\displaystyle x|_0^w=w-0=w$.

3. Re: Can someone explain this integral?

Hi and thanks for your reply. I see what you are saying I think, but if that is so, what is the difference between

$\displaystyle \int_0^w 1 \ \mathrm{d} x$

and

$\displaystyle \int_0^w \mathrm{d} x$

?

Are these equivalent?

Thanks again for your time. MD

4. Re: Can someone explain this integral?

Yes, they are equivalent.