The area under a curve is a fundamental concept in calculus that allows us to find the total quantity, or area, represented by a function between two given points. It provides a way to measure and analyze continuous data. The area under a curve is found using integrals, which are mathematical tools used to calculate the signed area between a function and the x-axis.

To understand the importance of finding the area under curves, let's consider a simple example. Imagine a car's velocity function plotted on a graph. The area under the curve of this function represents the total distance traveled by the car during a specific time interval. This information can be crucial for various real-life applications, such as determining fuel consumption or estimating travel time.

To find the area under curved functions, we need to employ integration techniques. Integration involves dividing the function into infinitesimally small rectangles and summing their areas (Riemann sums) to get an approximate value. As we decrease the width of these rectangles, the approximation becomes more accurate.

Remember, the area under curves is a powerful tool used in numerous fields of study, including physics, economics, and biology. In the upcoming posts, we will explore different methods for approximating the area under curves and delve into their real-life applications.

Let's get ready to discover the fascinating world of integrals and the area under curves!