A Brief Introduction to Calculus: Part 2.3 - Area Bounded Multiple Curves and/or Lines

  • Math
  • Calculus
  • Further Math
Published on Sat Aug 06 2022. Views
If you're new to calculus and know nothing about it, then this blog is aimed to get a gist of it for you, but not to turn you into a master of calculus.

Introduction

This series would primarily focus on the three fundamental areas of calculus - derivatives, limits, and integration, looking briefly at some of the different concepts to get started with calculus.; thus no prior knowledge of calculus is needed.

This is the third chapter of the second part of the series, and it is about finding the area bounded by multiple curves or lines.

Further content on this topic will be published in separate articles for performance reasons.

So now, let's sit back, relax, and have some fun!

Quick Access

Area Between a Curve and Another Line/Curve

The formula for calculating the area between a curve and a line(or another curve), in the x interval [a,b][a, b] is as follows:

aby1y2dx\begin{align*} \int_{a}^{b} y_1 - y_2\, dx \end{align*}

Where y1y_1 is the function of the curve/line above y2y_2.

Consider the following region:

In this case, y1y_1 is the function of the curve and y2y_2 is the function of the straight line, since in the required region, the curve is above the line.