Mastering Calculus: The Fun Way!

Calculus might seem like a scary monster at first, but it's actually a friendly giant. Let's break it down into bite-sized pieces so you can see there's nothing to be afraid of!

In this world there is d and ∫. So we have characters. Let's meet them.

Character 1: d

This character is like a tiny helper who means “a little bit of”

• So, dx means a little bit of xa large bit of x
• du means a little bit of ua large bit of u

You can also think of "d" as being indefinitely small.

Character 2: ∫

This one might look like a fancy scribble, but it's just a stretched-out S that means “the sum of”,

• So, ∫dx means the sum of all the little bits of xthe difference of all the little bits of x
• ∫dt means the sum of all the little bits of tthe difference of all the little bits of t

That's it. These are the characters you need for calculus.

Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx.

If you add them all up together you get the sum of all the dx's, (which is the same thing as the whole of ).

You have tiny pieces called dx. When you put all those pieces together, you get the whole puzzle.

Try it, click on any piece and see them arranged.

Reset

The Whole

Think of "integral" as meaning “the whole.” For example, if you think of one hour, it's made up of 3600 little bits called seconds. When you add up all those seconds, you get the whole hourthe whole minute.

Whenever you see the ∫ symbol, remember it's just telling you to add up all the little bits that follow. Easy peasy!

Can you convert the following sentence to calculus?

Sum of little bits of m: ∫dmd∫mm∫d

Recap

1. d means "a little bit ofa lot of."
2. ∫ means "the sum ofthe difference of."
3. Putting all the little bits together gives you the whole thingnothing.

That's it! Now you know the secret to understanding calculus. Go ahead and conquer those math problems with confidence!

Why Calculus

But why do we need to find "a little bit of (dx)" something or "sum of" something? Consider rectangle below:

If we have to guess, its area is 12 units 16 units8 units

What about the circle below:

A circle does not have clean edges. So finding it's area is hardeasy.

So how can we find an area of a circle?

So we used our two new characters and found out the area of a circle.

First, instead of trying to find the area all at once, we broke it down into small wedges. So we a got a little bit of lot of wedges.

Then when we do a sum of difference of all the little bits of wedges, we get the area of the circle.