Integral Calculus Primer

The study of integral calculus is perhaps best introduced by translating the word calculus which comes from the Latin phrase which means ‘small stone’. Calculus is generally split into two main sections – Differential Calculus and Integral Calculus. The former splits problems into small pieces to try and understand how it changes whereas Integral calculus joins the pieces together to try and understand the sum of the parts.

Integral calculus is used to solves a series of problems found anywhere;

  • How do you work out the area of a curve?
  • How can you work out the length of the curve?
  • How fast is something falling?
  • Where will a thrown object land?

You can use the tools covered in integral calculus to work out problems like this and many others. The core idea to remember though is they are all about ‘changes’ – changes in speed, distance, height and so on. The below video demonstrates what is meant by the area under the curve and how you can use simple rectangles to define the area. It included simple examples using a spreadsheet program to calculate – it is a very well done and important introduction to integral calculus.

There are lots more great examples that you can find both on YouTube and on the various educational sites, if you can’t get access based on your location try this which shows you a VPN that isn’t banned by the majority of sites like Netflix and others.
Integral calculus is used to assign values to functions specifically to try and calculate changes in area, volume and similar concepts that can be described by adding small changes together.

There are two main operations which are used here – integration and it’s inverse differentiation. This is no new mathematical concept, indeed the first principles of integration were determined by no less than Isaac Newton and Gottfried Leibniz in the end of the 17th Century. The concept and practice have of course been further developed up to the present day by people like Bernhard Riemann who produced the first comprehensive mathematical definition.

Further Reading

Too Much Math Is a Bad Thing for Young Minds

Taking Calculus senior year in high school officially turned me off to math, as it probably does for many high schoolers.  While the practicality and logical application of other math subjects is obvious, Calculus is just too advanced for practical application.  While it’s great for future math majors, its complexity and disconnect with the real world make it off-putting.  In fact it could be argued that forcing teens to take advanced math is partially to blame for our crisis with STEM.

Basic math is critical for survival; that was true long ago and it certainly still holds true today.  Even the most basic activities in the home in some way or another intersect with basic math.  Whether it’s your printer telling you that your ink cartridge has just one-quarter left to go, or your attempt at filling out a bank deposit slip for several checks you received, it’s critical that you understand basic math to carry on.

Perhaps if high school and even college classes were most focused on the practical application of concepts in the real world, or even based more around current events, students would be more likely to comprehend and apply what they are learning.  Generally speaking the education system (at least in the US) is broken, primarily because it’s taking too long to evolve.