Leibniz integral rule

Leibniz integral rule is a fancy way of saying that if you have a math problem with two things that change, like one thing going up and the other going down, you can use something called a formula to figure out how much the whole thing changes.

Let's say you have a seesaw with one side going up and the other going down. If you want to know how much the whole seesaw is changing, you can use the Leibniz integral rule to figure it out.

The formula looks like this:

d/dx [ integral from a to b of f(x,t) dt ] = integral from a to b of df(x,t)/dx dt

Don't worry if that looks confusing, we're going to break it down.

The 'd/dx' part just means that we're trying to figure out how much something changes when we change x.

The integral sign (∫) is just a fancy S that tells us we're going to be adding up a bunch of things.

The 'f(x,t)' part is just a fancy way of saying that we have a math problem with two things that change - 'x' and 't'.

The 'a to b' part shows us that we're only looking at the math problem between two specific points.

The 'df(x,t)/dx' part is another fancy way of saying that we're figuring out how much the math problem changes when we change 'x'.

Putting it all together, the formula is telling us that if we want to figure out how much the whole math problem changes when we change 'x', we can add up all of the little changes in the problem between points 'a' and 'b'.

So, just like how we can figure out how much the seesaw changes when one side goes up and the other goes down, we can use Leibniz integral rule to figure out how much a math problem changes when we change one of the variables.