Definition: A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

Alright class, settle down, let’s take a look! That dictionary definition – it's quite a mouthful, isn’t it? Let’s break it down and make it easier to understand. Don't be overwhelmed by all those words! Essentially, “integral” in math is about accumulation . Think of it like this: Imagine you’re building something brick by brick. You have a pile of bricks (that’s your function!), and you want to know how much total material you have. You could count each brick individually – that's like the "sums computed." But what if you divided the area where you were building into tiny little squares? You’d measure the area of each small square (that’s the “measure of that subset”) and then multiply it by the number of bricks in that square. Then, you'd add up all those little pieces – that’s the "summed products." The integral is the result of that whole process. It gives you a single number representing the total amount – like the total volume or area you created. Let's rhyme it out for a bit: "An integral, a wondrous thing, Calculates areas, makes numbers sing! Dividing up in little parts, Adding them together, playing our arts!" Here’s a simpler way to think about it: Function: Think of a line going up and down. Subset: Imagine slicing that line into very thin rectangles. Measure: The width of each rectangle. Product: The area of each rectangle (width times height). Sum: Adding up the areas of all the rectangles. The integral is the total area under that curve – it's a way to find the accumulated value. Do you have any questions about this? Don’t be afraid to ask! It takes time to grasp these concepts, so let's work through them together.