Calculus can be kind of tricky when you're first learning it. Here's how you can use spreadsheet programs to your advantage. Use this to check your answers or just get an idea of what a graph looks like. If you're doing integration then you also probably know that there are some functions that don't have elementary antiderivatives. You can use spreadsheets to visualize what the antiderivatives of these functions looks like.

Just a quick note: throughout this instructable I refer to myself as we. This isn't the royal we, I'm doing this project with a group of 3 other people for a class at UBC, so when I say we I mean us, my group.

Just a quick note: throughout this instructable I refer to myself as we. This isn't the royal we, I'm doing this project with a group of 3 other people for a class at UBC, so when I say we I mean us, my group.

First thing you're going to need is a spreadsheet program like Excel, Numbers, or OpenOffice. If you don't know how to use any of these programs, don't worry, it's pretty easy learning.

To demonstrate, we're going to use the equation y=2x^{3}+6x^{2}-12x+4. It's the same equation shown in the picture below, which looks a lot nicer. We chose this equation because finding it's derivative and antiderivative will be easy, so we can check our answer.

First, you want to put your x values down in your spreadsheet, I made mine go from -5 to 5. Also set your step size, I set mine at 0.1. You could also use 0.01 (it would be a bit more accurate) but you generally don't want to go smaller. Once your columns are more than a few thousand cells long, it takes forever for your computer to process them all at once. For my computer, below 1000 cells usually works well.

Put your step size in a cell (I use A2). Put your initial value at the top of the next column over, the second picture below shows you what this should look like. Then in the cell below (B2) type in "=B1+$A$2" without the quotation marks, hit enter. The dollar signs tell your spreadsheet program to reference A2 regardless of which cell you copy the equation into. Place your cursor over the bottom-right corner of the cell, there should be a small black square, click it and drag it down, as you drag it, you should see the numbers slowly getting bigger. It's hard to describe, look at the third picture. Drag this box down until you reach the other end of your X range, in this case 5.

To demonstrate, we're going to use the equation y=2x

First, you want to put your x values down in your spreadsheet, I made mine go from -5 to 5. Also set your step size, I set mine at 0.1. You could also use 0.01 (it would be a bit more accurate) but you generally don't want to go smaller. Once your columns are more than a few thousand cells long, it takes forever for your computer to process them all at once. For my computer, below 1000 cells usually works well.

Put your step size in a cell (I use A2). Put your initial value at the top of the next column over, the second picture below shows you what this should look like. Then in the cell below (B2) type in "=B1+$A$2" without the quotation marks, hit enter. The dollar signs tell your spreadsheet program to reference A2 regardless of which cell you copy the equation into. Place your cursor over the bottom-right corner of the cell, there should be a small black square, click it and drag it down, as you drag it, you should see the numbers slowly getting bigger. It's hard to describe, look at the third picture. Drag this box down until you reach the other end of your X range, in this case 5.

<p>Thanks for posting! This tutorial helped me re-learn how integrals are approximated. You rock!</p>

<p>Nice example and ideas. I gussied up the spreadsheet a little. Needs a macro or two (on the integral from/to) to ensure valid input but it's a little better.</p>

Is add Image working fine?, or I used it wrongly, so It did not work for me? I do not know. <br> <br>Now it works fine. My error was that I posted my first comment without uploading the selected image file. However, the image does not appear in the 'preview'. Is that normal? I will see when this comment is posted.

I like this simple approach very much. Many people forget about math after graduation, but those who are in research and or any job related to calculation may also forget many basics and need from time to time to go back through to review the issue in a different way other than that usually given in the class-room, and the spreadsheets are essential tool in their everyday life. Your effort is not lost, on the contrary it is appreciated. I posted your site to my site on Facebook. I am sure many people will refer to your site some time ahead.

I know a lot of people could benefit from this. Having just graduated from college a bit ago I cannot believe I never learned this (or even thought to do it!) This is a great way to teach basic calculus. Great tutorial. I'm gonna pass this info along to my college buddies still going through. <br />

This was very helpful. Thank you.

This is EXCELLENT!
Once again I am puzzled as to why some Instructables get to be "featured" when some really good ones, like this one, are passed over.

I'm flattered. I do admit that this instructable is lacking the "fun factor" of most instructables. It's pretty boring unless you're really into math. Thanks though.