Spreadsheet Calculus: Derivatives and Integrals

Step 5: Let's do a definite integral

If you're in a calculus course, you're probably going to be asked to do a few definite integrals. Basically you integrate from one x value to another. Using the integral you just made, checking your answer can be pretty easy. For example, let's try the integral shown below. This is the one we just plotted earlier. If you already know how to integrate, solve it by hand, you should get 92.5.
To approximate it with out spreadsheet, we just write (in any cell) "=F81-F31". Row 81 is where x=3, row 31 is where x=-2. What you're doing is taking the indefinite integral at x=3 and subtracting the indefinite integral when x=-2 from it.
On this spreadsheet the answer we got was 94.58. Not a bad approximation, but it wouldn't get you any points on a homework assignment (unless you're asked to approximate a function using finite sums.) If you use a 0.01 step size you get 92.70, even more accurate. Using 0.001 step size you get 92.52, which is even more accurate. Trying smaller step sizes would just be ridiculous though, it would take a few hundred thousand cells, it would take your computer a while to figure it out.
I've attached the demo spreadsheet below. Enjoy.