1. ## Verbal Problem

My homework includes a verbal problem I am trying to decipher:

"Let f and g be continuous functions on [a, b] and let g(x) ≤ f(x) for all x in [a, b]. Write in words the area given by ∫[f(x) - g(x)]dx (evaluated from a to b).
Does the area interpretation of this integral change when f(x) ≥ 0 and g(x) ≤ 0?"
I'm trying to figure out how to answer this. I am seeing this as two "vertical" functions next to each other, such that the area should be calculated as an integral with respect to the y-axis. And that the area would be reduced from the absolute value if f(x) ≥ 0 and g(x) ≤ 0, because some amount of negative area would result (resulting in either an area of 0, negative area, or some amount of positive area less than the absolute value of the initially given scenario.)

Am I understanding that correctly? Am I missing something? Even if I do understand it, is there some way to say that more clearly?

2. probably not. $\displaystyle g(x)<0$does not mean the area is negative.
Because the area is related to $\displaystyle f(x)-g(x)$, which is irrelevant with whether $\displaystyle g(x)>0$or$\displaystyle g(x)<0$
if the intergral is $\displaystyle \int g(x) \ dx$ then it will be negative when $\displaystyle g(x)<0$

3. Nevermind, I get it now. I was mis-interpreting the question and making it WAY more complicated than it is. Duh.