# Homework Help: Simpson & trapezium rule

1. Mar 2, 2005

Why should I use the simpson or trapezium rule when calculating the area under a curve? It is much easier and accurate when using integration the ordinary way

2. Mar 2, 2005

### Justin Lazear

In general, you must approximate something that is either difficult or impossible to do analytically. Not many functions can be "integrated the ordinary way." Most functions can be approximated, though.

--J

3. Mar 2, 2005

Can you give me an example of a function that is impossible to integrate analytiacally?

4. Mar 2, 2005

### Justin Lazear

$$\mbox{Si}(z) \equiv \int_0^z \frac{\sin{t}}{t} dt$$

--J

Last edited: Mar 2, 2005
5. Mar 2, 2005

### HallsofIvy

$$\int_0^1 e^{x^2}dx$$

"Almost all" integrals cannot be done analytically.

6. Mar 2, 2005

### arildno

However, "almost all" integrals you learn about in your first year can be solved by the "ordinary" way..

7. Mar 2, 2005

### scholzie

Perhaps more tangable to you in the near future: If you are learning Simson's rule now, you will most likely get to arclength very shortly. You will also find then that sometimes evaluating an integral like

$$\int_a^b\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}{dx}$$

Can be very difficult if $\frac{dy}{dx}$ is long or confusing.

Last edited: Mar 2, 2005