From the course: Complete Guide to Calculus Foundations for Data Science
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Area under the curve
From the course: Complete Guide to Calculus Foundations for Data Science
Area under the curve
- [Instructor] Now that you know what integrals are, let's take a closer look at a common interpretation of them, the area under the curve. This interpretation tends to be the most intuitive and straightforward to understand. Let's dive in. In order to look at this interpretation, you will have to use definite integrals since this interpretation does not work for indefinite integrals due to the potential for infinite area. Let's say you have a function f of x with an integral of the integral of a to b of f of xdx, over the interval that's closed and bounded a to b. The result of this integral represents the total area between the curve of f of x and the x-axis given by the bounds of a and b. Let's take a look at this graphically. Let's say you have the function f of x equals 2 multiplied by x plus 1, and you want to look at it with the bounds of x being between 1 and 3. In the graph, you'll see you have the line of the function, and then the shaded area is going to be between those…
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