### Further Web Resources

Check out "National Curve Bank" for a nifty animation of volumes of revolution

### Wolfram Alpha

The easiest way to explain the power of the Wolfram Alpha site, I think, is to show you some examples:

Derivatives

- derivative
of x
^{4}sin x – be sure to click on "show steps" - derivative evaluated at a point of (1 + sqrt(x))^7 at x = 4
- second derivative of sin(2x)
- implicit differentiation dy/dx for x^2 + y^2 = 1

Integrals

- an indefinite integral – be sure to click on "show steps"
- a definite integral – if you want to see the steps, make it an indefinite integral instead

Graphs

- a graphing example – if the complex parts of the graph confuse you, try adding a domain restriction
- multiple lines on the graph

The beauty of the Wolfram Alpha engine is that it's very forgiving in terms of syntax. In fact, the less you type into the search box, the more information it gives you. For example, to graph an equation, you just need to type the equation into the search box and it will automatically be plotted for you. To start using Wolfram Alpha, I recommend using one of the above links and then modifying the text in the Search Box to get the expression/equation you are interested in.

Two dangers to be aware of:

- When Wolfram Alpha outputs "log(x)", they actually mean "ln(x)" or "log
_{e}(x)". - A lot of the graphs contain the curves for complex values of the variable as well as real.

Note: you can also branch out and ask questions like: What is the answer to life, the universe, and everything?

### For Other Classes

#### Mech

Here are some links to pages showing how to find the arclength of a parabola:

- Wolfram Alpha – shows how to compute the integral you need to find – be sure to click on "show steps" to see the details (note also that their "log" means natural log (ln))

#### Civil

Here's a quick explanation of how to rewrite a nasty integral from your Statics class into something you can integrate using methods from Math 187.