Singular integrals

Okay, so imagine you have a book with lots of words and pictures in it. That's like a function, which is a thing that gives you an answer when you put in a number.

Now imagine you want to find out how much ink was used to print all the words in the book. You could count each letter and then add them up, but that would take a long time if there are lots of words.

A singular integral is like a shortcut that tells you the answer without having to count everything. It looks at just one part of the book, like a sentence or a paragraph, and uses that to figure out how much ink was used in the whole book.

But sometimes there are parts of the book that are different from the rest, like a picture or a big title. Those parts are called singularities because they don't fit the pattern of the rest of the book.

When you have a singular integral, you need to be careful not to count the singularities too much or too little. It's like if you were counting apples in a basket, but then you saw a banana in there too. You wouldn't want to count the banana as an apple, but you also wouldn't want to ignore it completely.

So, in math, a singular integral is a way to find an overall answer by looking at smaller parts, but you have to be careful not to mess up when there are weird parts in there.