# Improper Integrals

• Nov 27th 2012, 03:26 PM
kasper90
Improper Integrals
Attachment 25963

Can someone give me a hint for this one ?
It's from Elementary Analysis by Ross.
• Nov 27th 2012, 03:46 PM
Plato
Re: Improper Integrals
Quote:

Originally Posted by kasper90
Attachment 25963
Can someone give me a hint for this one ?
It's from Elementary Analysis by Ross.

Look at theorems 33.4 & 33.5.

You know that $f(x)\le |f(x)|.$
• Nov 29th 2012, 03:49 PM
kasper90
Re: Improper Integrals

1. Let h := |f| - f
2. h is continuous on (a,b) (as |f| and f are)
3. 0 <= h <= 2 |f| (as -f <= |f| )

than use 36.6 ?
than integral h exist
than integral h - |f| exist (as |f| exist)
and integral f exist