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13.1 The First Fundamental Theorem

If f is continuous on a closed interval [a, b] and F' = f then




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. 



Example 5

Example 6

Example 7