The Fundamental Theorem of Calculus (Part 2)
FTC 2 relates a definite
integral of a function to the net change in its antiderivative.
Fundamental
Theorem of Calculus (Part 2): If $f$ is
continuous on $[a,b]$, and $F'(x)=f(x)$, then $$\int_a^b
f(x)\, dx = F(b)  F(a).$$ 
This FTC 2 can be written in
a way that clearly shows the derivative and antiderivative
relationship, as
$$\int_a^b g'(x)\,dx=g(b)g(a).$$
This gives us an incredibly powerful way
to compute definite integrals:
 Find an antiderivative.
 Evaluate it at the limits of integration.
This computation is the most important use of FTC
2 in this course.
Example: DO:
use the FTC to evaluate $\displaystyle\int_1^3 3x^2\,dx$.
The following video gives examples of using FTC
2 to evaluate definite integrals.
The following video explains FTC 2.
