




If f is continuous on a closed interval [a, b] and F' = f then
Notation:
This theorem implies that all techniques available for computing antiderivatives can be used_{ }to compute definite integrals, ie areas under curves.
Use of the theorem to compute areas:
_{Example 1 }
_{Example 2}
_{Example 3}
_{Example 4}
In particular, we can apply the substitution method to computing areas._{ }
Substitution:
_{Example 5}
_{Example 6}
_{Example 7}