# Integrals of Nonpositive functions

• March 7th 2010, 02:19 PM
10roye
Integrals of Nonpositive functions
show that if "f" is integrable then f(x) is less then or equal to 0 on [a,b] is equal to the integral from a to b of f(x) dx is greater then or equal to 0
• March 7th 2010, 09:24 PM
CaptainBlack
Quote:

Originally Posted by 10roye
show that if "f" is integrable then f(x) is less then or equal to 0 on [a,b] is equal to the integral from a to b of f(x) dx is greater then or equal to 0

CB
• March 8th 2010, 03:38 AM
HallsofIvy
• March 8th 2010, 04:38 AM
CaptainBlack
Quote:

Originally Posted by 10roye
show that if "f" is integrable then f(x) is less then or equal to 0 on [a,b] is equal to the integral from a to b of f(x) dx is greater then or equal to 0

Since $f(x)=-1$ fits the conditions and assume $b>a$, then $\int_a^b (-1) dx=(a-b)<0$ this cannot be true in general.

CB