If [tex]\int _{-\infty} ^{\infty}f(x)\: dx[/tex] is convergent and [tex]a[/tex] and [tex]b[/tex] are real numbers, show that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int _{-\infty} ^a f(x)\: dx + \int _a ^{\infty}f(x)\: dx = \int _{-\infty} ^b f(x)\: dx + \int _b ^{\infty}f(x)\: dx[/tex]

I'm clueless on how to show it other than by drawing what is stated: a generic finite integral being split into two finite pieces for each arbitrary point. Is there any other way to approach this problem?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Improper integrals

**Physics Forums | Science Articles, Homework Help, Discussion**