## Before You Watch

Before watching this video, make sure you’ve seen Introduction to Calculus. In fact, even if you’ve already seen it, it’s a great idea to watch it again! A lot of the notation introduced in that video is used in this one. This video also builds on the key concept of calculus that was explained in the introduction. So we suggest you watch Introduction to Calculus, then come back.

## Now What?

This video builds on Introduction to Calculus and discusses the core ideas of integral calculus, which is one of the two main branches of calculus. If you haven’t already done so, work through the videos covering the other branch of calculus, differential calculus. Start with Rates of Change and Differentiation.

Alternatively, if you’ve already seen those videos, the next step is to build up your ability to differentiate. You can do this with the Khan Academy at https://www.khanacademy.org/math/differential-calculus/taking-derivatives . It is easiest to learn how to integrate by first learning to differentiate. This is because integration is the inverse operation to differentiation, in the similar way that division is the inverse operation to multiplication.

## But When I am Going to Use This

Calculus is the mathematical study of how things change relative to one another. It has enormous applications in all areas of engineering and science, and is necessary knowledge to study for a degree in engineering or science.

Specifically looking at integral calculus, integration allows us to move from a rate of change and convert that into an absolute quantity. For example, calculus allows the measurement of a car’s speed over time (using it’s speedometer) to then be converted into distance (as measured by the odometer). Another example is the measurement of the speed of water flowing through a pipe, which can then be used to calculate the total amount of water that flowed through the pipe.