Improper Integrals: Struggling to Understand Convergence

[Zamael88]

Homework Statement

I don't understand why the following intergral is improper
http://img413.imageshack.us/img413/1667/38410700.jpg

I have a graph for the function.
http://img413.imageshack.us/img413/2424/photoxxs.jpg

According to this graph, the function should converge in [-∞,0)
However, my solution manual says that the function has an infinite interval of integration.

Could anyone tell me what I am mistaken?

Thank you for reading.

 

[benorin]

Improper integrals may either converge or diverge, that is, have a finite value or not. An improper integral is an integral involving an infinity in either or both bounds, or one whose integrand is discontinuous over the interval.

 

[Zamael88]

Oh I should have studied more.

Thank you. :)

 

[HallsofIvy]

"Infinite interval of integration" simply means that you are integrating from -infinity to 0, an infinite length.