- #1

- 58

- 0

## Main Question or Discussion Point

As I understand it, the following is true:

[tex]

\int_{0}^{\infty}{u(t - \lambda) d\lambda} =

\int_{0}^{t}{d\lambda}

[/tex]

But I do not understand why. It seems to me that the left side above should equal

[tex]

\int_{\lambda}^{\infty}{d\lambda}

[/tex]

since

[tex]

u(t - \lambda) =

\left\{\begin{array}{cc}0,&\mbox{ if }

t< \lambda \\ 1, & \mbox{ if } t> \lambda \end{array}\right.

[/tex]

I obviously don't understand this correctly. What am I not doing right?

[tex]

\int_{0}^{\infty}{u(t - \lambda) d\lambda} =

\int_{0}^{t}{d\lambda}

[/tex]

But I do not understand why. It seems to me that the left side above should equal

[tex]

\int_{\lambda}^{\infty}{d\lambda}

[/tex]

since

[tex]

u(t - \lambda) =

\left\{\begin{array}{cc}0,&\mbox{ if }

t< \lambda \\ 1, & \mbox{ if } t> \lambda \end{array}\right.

[/tex]

I obviously don't understand this correctly. What am I not doing right?