## Why do we need to study Integration?

The Petronas Towers

of Kuala Lumpur

Often we know the relationship involving

**the rate of change** of two variables, but we may need to know the

**direct** relationship between the two variables. For example, we may know the

**velocity** of an object at a particular time, but we may want to know the

**position** of the object at that time.

To find this direct relationship, we need to use the process which is

**opposite** to differentiation. This is called

**integration** (or

**antidifferentiation**)

*.*
The processes of integration are used in many applications.

The

**Petronas Towers** in Kuala Lumpur experience high forces due to winds.

**Integration** was used to design the building for strength.

Sydney Opera House

The

**Sydney Opera House** is a very unusual design based on slices out of a ball. Many

**differential equations** (one type of integration) were solved in the design of this building.

Wine cask

Historically, one of the first uses of integration was in finding the

**volumes of wine-casks** (which have a curved surface).

Other uses of integration include finding areas under curved surfaces, centres of mass, displacement and velocity, fluid flow, modelling the behaviour of objects under stress, etc.