What is an integral?

Question

I need to research for my AP class this summer but every website I go to has a 30 page explanation on what an integral is. Can anyone help me with simple, basic terms? I just need a small idea on what it is for me to be able to build my essay. Thanks. :D

Answer 1

An integral is a way of finding area under a curve.  If you wanted to find the area of a rectangle you would multiply the base times the width.  But what if you didn't want the area of a rectangle, you wanted the area of a shape with a squiggly border?  You could imagine putting hundreds of rectangles underneath the squiggly border with very small widths so that if you added the area of all of those rectangle they would approximate the area of the shape.  An integral is a way of computing this area (look at the article on wikipedia for a picture of these small rectangles under a curve.)  You can use it in many ways.  For instance, integrals help you to find area between curves, the length along a curve instead of along a straight line (like the length of the coast), or to find the volume of nonstandard shapes.  

Hope this helps you!

Answer 2

the difference between the values of the integral of a given function f(x) for an upper value b and a lower value a of the independent variable x