My homework includes a verbal problem I am trying to decipher:
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.)"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?"
Am I understanding that correctly? Am I missing something? Even if I do understand it, is there some way to say that more clearly?