"Finding Areas by Integration" is a mathematical technique used to calculate the area under a curve or between two curves. It involves using calculus to find the definite integral of a function, which represents the area between the function and the x-axis.
Integrating a function allows us to find the exact area under a curve, which can be useful in various fields such as physics, engineering, and economics. It also helps us to understand and analyze the behavior of a function over a given interval.
The first step is to determine the limits of integration, which define the interval over which the area is to be calculated. Then, we need to find the indefinite integral of the function. Next, we substitute the limits of integration into the indefinite integral to get the definite integral, which represents the area. Finally, we evaluate the definite integral to obtain the numerical value of the area.
No, integration can only be used to find the area of continuous functions. If the shape is not a continuous function, we can divide it into smaller continuous sections and integrate each section separately to find the total area.
Finding areas by integration is used in various fields such as physics (to calculate work and energy), engineering (to calculate volumes and surface areas for 3D shapes), and economics (to calculate the area under a demand curve, which represents consumer surplus).
