# Question #e8b51

##### 1 Answer

One has to do with instantaneous rates of change, while the other mainly deals with the sums of very small components. Or when you have to find the opposite of a derivative.

#### Explanation:

Covering the obvious ones...

Let's suppose you have a distance-time graph:

graph{0.25x^2 [-6.06, 16.44, -2.43, 8.815]}

And you had to find the velocity at

Since velocity is a rate of change, or the *slope*, and we have to find the slope of a point

or the *derivative* of the function

Now, let's suppose you have a question like:

What is the change in velocity of an object in free fall from

Well, we know that all objects accelerate at

So, the derivative of *what* will give us

In that case, the *what* is the integral of

But we wanted to find the *change* in velocity.

So, we take the difference in the velocity from 0 to 10.

Writing it in shorthand would be:

What's fascinating is that the area under that line 9.8 represents the *change in velocity*.

Integrals can also be used to find the sum of things divided into very small parts. I'm pretty sure you're familiar with the ol' finding the area under the curve thing.

The sum of all the blue rectangles would be the integral of an interval of the function.

Those are the basics.