Multiple integrals allow for the calculation of volumes in higher dimensions from "summary" of Skills in Mathematics - Integral Calculus for JEE Main and Advanced by Amit M Agarwal
Multiple integrals are a powerful tool in calculus that extend the idea of a single integral to higher dimensions. They are used to calculate various quantities such as volume, area, mass, and moments in multiple dimensions. When dealing with volumes in higher dimensions, we can use double integrals for three-dimensional objects and triple integrals for four-dimensional objects. In the context of volume calculation, multiple integrals allow us to break down the volume into infinitesimally small pieces and sum them up to find the total volume. This is similar to how a single integral can be used to find the area under a curve by dividing it into small rectangles ...
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