Rewriting an Integral Let be convergent and let and be real numbers where Show that

Chapter 8, Problem 111

(choose chapter or problem)

Rewriting an Integral Let \(\int_{-\infty}^{\infty} f(x) d x\) be convergent a and b let and be real numbers where \(a \neq b\). Show that

\(\int_{-\infty}^{a} f(x) d x+\int_{a}^{\infty} f(x) d x=\int_{-\infty}^{b} f(x) d x+\int_{b}^{\infty} f(x) d x .\)

Text Transcription:

Int_-infinity^infinity f(x) dx

a neq b

Int_-infinity^a f(x) dx + Int_a^infinity f(x) dx = Int_-infinity^b f(x) dx + Int_b^infinity f(x) dx