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.
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.
Maths Is Fun has a great page that covers the basic concepts of integration. It then extends your learning by demonstrating how to perform the integrations, which is an important skill.
IntMath gives a good explanation of the process of integration, as well as covering the methods of integration. It provides some excellent examples of applications of calculus that are in common use today, and includes applets to help your understanding of both differential and integral calculus.
The Khan Academy has a comprehensive set of video tutorials covering a wide range of mathematical and other concepts, as well as questions to test your knowledge. This content provides a whole chapter on taking the derivatives, including of harder equations not covered in this video.
Patrick JMT (Just Maths Tutorials) has an extensive set of video tutorials covering a large range of mathematical concepts. This content covers the basic concept of integration. The site also offers a wide selection of other videos covering several integration topics and techniques.