Evaluate the definite integral (x^3-x)dx with bounds 1 to 5 by the limit definition of a Riemann Sum.
We break the interval into n steps:
We then form each little rectangle for the area. The area of the ith rectangle will be
where
So this is
So the estimate of the area will be
which is exact when taking the limit:
There's a lot of simplifying to do but the process is otherwise simple.
-Dan