Geometric meaning of reversing the limits of an integral

In summary, the conversation discusses the concept of reversing limits in integrals and how it affects the value of the integral. It is explained that geometrically, reversing the limits means changing the orientation of the area being measured, which can result in a negative area if the direction is against the positive x-direction. The conversation also touches on the concept of orientation in mathematics and how it is important to consider it when performing calculations. The difference between calculus as a framework for calculations and calculus as analysis is also briefly mentioned.
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Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function and the plane that contains ...Integral Calculator
 

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