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Mangesh posted an Question

June 09, 2020 • 02:28 am

30 points

CSIR NET
Physical Sciences

Mathematical physics

please explain me the physical significance or geometric interpretation of volume integral in vector calculus

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Dhairya sharma

see example.
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here is the example
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will help u
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Chandra prakash

When you speak about volume you require 3-dimensions. The form of the volume integral depends on the coordinate system. And the coordinate system chosen depends on the geometry of the 3-D object. For rectangles, cubes and other similar objects we would use Cartesian coordinates, while for spherical geometries the spherical coordinate system would be employed. Of course you can use any of these or other coordinate systems on any shaped objects, but the calculation are usually simpler with the proper coordinate system. Now for Cartesian coordinates the the volume integral is: and for spherical coordinates the volume integrates;
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Chandra prakash

In mathematics—in particular, in multivariable calculus—a volume integralrefers to an integral over a 3-dimensional domain, that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities.
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dear I hope u understood it
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Dhairya sharma

see attached
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see attached
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thanx
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Chandra prakash Best Answer

A volume integral over V with density of whatever as integrand is the total amount of whatever that is in V. Such integrals are commonly encountered. In particular, the volume integral of charge or mass density gives the charge or mass of in that volume. You also encounter moments.
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I hope you understand
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thanx
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Dhairya sharma

basically it's significance is that when we have small element or perameter of perticular geometry we can find out whole volume
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Dhairya sharma

volume integral refers to an integral over a 3-dimensional domain, that is, it is a special case of multiple integrals.
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which gives us volume on integration
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