This page, like many others on this site, is under major construction. Right now, it pretty much just consists of my lecture notes.

**EXAMPLE | The stereotypical example**

Use midpoint, trapezoidal, and Simpson's methods to approximate,

**by hand**, \[\int_0^2{e^{x^2} dx}\] using \(n = 4\). Compute the error bounds (yes, they are going to be ugly) and compare these to the actual errors using the fact that the value of this integral is approximately 16.45262776.

**EXAMPLE | "Excel"ing through integration**

Now use excel to compute the same integral, but using \(n = 20\).

Take a look at my Excel file.

**EXAMPLE | Numerical integration using WinPlot**

Again, the same example, but with WinPlot. Note: the error bounds are not possible to find using WinPlot.

**EXAMPLE | Getting \(n\) just big enough**

How large do we have to take \(n\) so that the approximations of \(T_n, M_n, \text{ and } S_n\) to the integral \(\int_0^{\pi}{\sin{(x)} dx}\) are accurate to within 0.00001?

The only other type of problem that you typically find requiring these techniques is data set problems.