confusing calculus problem?
What is the area (a positive number) between the x-axis and the graph of f (x) on [3, 5] if f (x) is a negative function whose antiderivative F has the values F (3) = 9 and F (5) = 4?
We did not go over this in class, and there aren't any examples of such problems in the textbook. 10 points to most helpful answer!
Comments
You must have gone over it. This is the Fundamental Theorem, or one version of it.
If f(x) = F'(x) ... F is an antiderivative of f, means f is the derivative of F
then the integral from x=a to x=b of f(x)dx = F(b) - F(a)
That's equal to F(5) - F(3) = -5 in your case.
That definite integral is the net area between f(x) and the x axis. You're given that f is never zero on that interval ("a negative function"), so there are no + and - areas to cancel, and your answer is
A = |F(5) - F(3)| = 5