# Fundamental Theorem of Calculus Part 2

• Aug 10th 2010, 12:51 PM
Chokfull
Fundamental Theorem of Calculus Part 2
Can anyone help me understand this?

The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or

Quote:

If f is continuous on [a, b], then the function g defined by

$\displaystyle g(x) = \int_a^xf(t)dt$ $\displaystyle a\le x\le b$
is continuous on [a, b] and differentiable on (a, b), and $\displaystyle g'(x) = f(x)$.

However, the FTC2 says that $\displaystyle \int_a^bf(x)dx=F(b) - F(a)$, where F is the antiderivative of f.

But why would it be the difference between two antiderivatives rather than just being an antiderivative in itself?
• Aug 10th 2010, 01:11 PM
Plato
Quote:

Originally Posted by Chokfull
Can anyone help me understand this?
The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or
However, the FTC2 says that $\displaystyle \int_a^bf(x)dx=F(b) - F(a)$, where F is the antiderivative of f.
But why would it be the difference between two antiderivatives rather than just being an antiderivative in itself?

What exactly does that question mean?
• Aug 10th 2010, 01:42 PM
Chokfull
Never mind i realized I was being stupid :P