Skip main navigation

Approximating areas under curves

What are integrals? This video gives a definition of integrals and explains what they are used for.

This week we are diving into a new topic, integrals. First, we will define integrals and their notation, how to calculate them and where to use them.

  • For a continuous function defined over an interval ([a,b]), the process of dividing the interval into (n) equal parts, extending a rectangle from the (x)-axis to the graph of the function, calculating the areas of the series of rectangles, and then summing the areas yields an approximation of the area of that region.
  • The definite integral can be used to calculate net-signed area, which is the area above the (x)-axis less the area below the (x)-axis. Net signed areas can be positive, negative, or zero.
  • The component parts of the definite integral are the integrand, the variable of integration, and the limits of integration.
  • (dx) indicates that (f(x)) is a function with respect to (x), called the variable of integration.
This article is from the free online

Applications of Calculus

Created by
FutureLearn - Learning For Life

Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now