# Tell me what integrals are

1. Oct 23, 2005

### suspenc3

Hi, my physics teacher has recently started putting integrals into all of his examples and notes, but we havent gotten to integrals in calculus yet.

Could anyone basically tell me what integrals are,. and what they are for

2. Oct 24, 2005

### *melinda*

hi,

The same thing also happened to me when I took physics and calculus concurrently. This is an oversimplification, but hopefully it will enough for now.

There are two types of integration; definite and indefinite.

Indefinite integration (also known as anti-differentiation) does exactly what its name implies.

Say you have a function and take its derivative. If you integrate the derivative, you will get the original function back. For example:

$$y = x^2$$

$$\frac {dy} {dx} = 2x$$

$$\int 2x \,dx = x^2 + c$$

where c is an arbitrary constant.

Definite integration is often used to find area. If you have a geometric shape, you can use formulas to find area.

But say you have the above function, $y = x^2$, and you would like to know the area of the region bound between the x-axis and the curve, between the points x = 0, and x = 1.

You can exactly determine this area by evaluating a definite integral.

One of the many uses of this in physics is to determine the work done by a variable force. Anyway, that’s where I first saw integration.