Definite integration

Definite integration follows the same normal steps as indefinite integration.

Steps

1. We first integrate the expression (but don’t add the +c term).
2. Then we substitute the upper limit into the integrated expression - the upper limit is at the top of the integral sign - the a in \int_a^b.
3. We next substitute the lower limit into the integrated expression - the lower limit is at the bottom of the integral sign - the b in \int_a^b.
4. Finally, we subtract the result of step 3 from the result of step 2 to get the final answer. We always take away the integral found from the lower limit from the upper limit.

Notation

If we have the unintegrated function we write it like this:

\int_b^a f(x) \, dx

If we let g(x) be the intergral of f(x), then we can write:

\left[g(x)\right]_b^a