i know that if a function lies below the x-axis, the area between the function and the x-axis is considered negative area. if two curves are below and x-axis, shouldn't the area bounded by those two curves be negative as well? how come the area between two curves is always positive?

2. Originally Posted by oblixps
i know that if a function lies below the x-axis, the area between the function and the x-axis is considered negative area. if two curves are below and x-axis, shouldn't the area bounded by those two curves be negative as well? how come the area between two curves is always positive?
It really depends on how you interpret the question.

There's no such thing as "negative area" - it's just saying that this area lies below the x-axis.

So yes, if you have two curves below the x-axis, the area bounded between them also lies below the x-axis, and thus should have negative sign to denote this.

But if you're asked for the AREA, you can NOT write it with a negative sign, because there's no such thing as negative area. Remember, Area is "How many unit squares lie in this region". Can you have a negative number of unit squares? Of course not.

If you're asked for Area, you can not write a negative sign unless it specifically asks you to denote whether it lies above or below the x-axis.