Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
where . Each interval has length
.
At these sampling points, the function takes on values of
We approximate the integral with the Riemann sum:
Recall that
so that the sum reduces to
Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:
Just to check: