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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.
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