Simpson's rule

Hello there! Do you want to learn about Simpson's Rule? Well, it's a way that mathematicians use to find out the area under a curved line.

Imagine you have a graph, with a curved line on it, and you want to know how much area is underneath the line. This area could represent the distance traveled by a car over time or how long a river is over a certain distance, for instance.

Now, Simpson's Rule is like a game where we are going to use some funny shapes called "parabolic curves" to estimate the area under the curved line. To create these shapes, we take three points evenly spaced along the curved line and draw arches through those points. These arches will almost look like an 'n' shape. This funny shape we drew inside the line is called a 'parabolic curve' or just a 'parabola'.

Then we calculate the area of all the parabolic curves we drew inside the line and add them up to get an estimate for the total area under our curved line. The more of these parabolic curves we draw, the more accurate our estimate will be.

So, basically, Simpson's Rule is just a fancy way to estimate the area under a curve on a graph. It's like a game where we draw funny shapes and use their areas to find out how much space is under the line. Hope that helps!