I can't say I understood your question, but refering to the title of the thread, the area between two 'well-behaved' functions f and g on the interval [a, b] is given with [tex]\int_{a}^b(f(x)-g(x))dx[/tex], if f(x) >= g(x), for every x from [a, b].NIZBIT said:I am trouble with problems that don't list each function f(x) or g(x). The book sets them equal to y. Every time I do these I'm getting them wrong. When I check the solution, I'm mistaking f(x) for g(x) or vise versa. So is there a way to tell which y is f(x) or g(x)?
What? Neither is "f(x)" or "g(x)" until you name them! Call whichever you want f and the other g. It might be that your textbook is using a convention that "f" is always the "upper" curve and "g" is always the "lower" curve so that the area is given by [itex]\int (f(x)- g(x))dx[/itex]. If that is the case, then determine which is above the other. Hint: the first is a parabola opening upward, the second a parabola opening downward. You need to decide which is the "upper" curve and which the "lower" curve. You will also need to determine where they intersect.NIZBIT said:This is what I'm talking about:
Find the area between these two curves-
y=x^2-4x+3
y=3+4x-x^2
Now how do you know which is f(x) or g(x)?