Pettis integral

Okay kiddo, have you ever drawn a graph with lines going up and down? That's what we use to show how things change over time, like a bumpy roller coaster track.

Now imagine you have some numbers or measurements you want to add up along that roller coaster track, like how far the roller coaster goes in total. But, the problem is that the roller coaster track is not a straight line, so you can't just add up the numbers like you would on a flat surface.

That's where the Pettis integral comes in. It's like a special way of adding up those numbers on the bumpy roller coaster track. Instead of just adding them all together, we divide the track into little pieces and add up the numbers for each piece separately.

But, since the track is bumpy, we can't just use a regular number to represent each little piece. Instead, we use something called a "function." Think of it like a set of instructions for how to calculate a number for each little piece of the track.

So, we use these functions to add up the numbers for each little piece of the bumpy roller coaster track, and that gives us the total distance the roller coaster traveled. And that's how the Pettis integral works! It's a way of adding up numbers on a "bumpy" surface using special functions.