CALCULATING, 'areas using integrals is a central application of calculus.'

CALCULATING, "areas using integrals is a central application of calculus."

Calculating areas using integrals is a central application of calculus. A common application is to determine the area between the graph of a function and the x-axis. This is done by integrating the function over the relevant region, which measures the area under the graph, with negative values ​​indicating that the area is under the axis. A similar calculation can be performed for the area between the graph and the y-axis, adjusting the integration process to fit the y-axis.

Another important use case is calculating the area between two graphs. Here, the difference between the two functions is considered, and the integral over the common region gives the area between the two curves. This is useful when you want to measure the space bounded by two different functions. In all cases, the integral allows you to perform complex area calculations that go beyond mere geometry and rely on the functions themselves.

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