I saw somewhere triple line integrals

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Triple line integrals refer to integrals over closed paths, surfaces, and regions in space, specifically denoted as \oint d\sigma for closed paths, \iint dS for closed surfaces, and \iiint dV for closed regions. The closed surface integral is used to integrate vector fields across a closed surface, while the triple integral is applied to vector fields over closed volumes, often encountered in vector calculus and electrodynamics. These integrals are essential for calculating quantities like volume and flux. Resources for studying these integrals can typically be found in undergraduate calculus and physics courses. Understanding these concepts is crucial for advanced applications in mathematics and physics.
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I saw somewhere triple line integrals, 3 integrals with a circle(the symbol) , may you tell me exactly what are called, to find & study them ?
 
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Those are NOT "line integrals".

\oint d\sigma is an integral over a closed path.

\skew{57} {\skew{15}\subset \supset} \iint \mbox{ } dS is an integral over a closed surface.

<br /> \skew{57} {\skew{15}\subset \supset} \iiint dV\mbox{ }<br /> is an integral over a closed region in space. If you are working in 3 dimensions to begin with, ALL regions are "closed" so the circle is not necessary.
 
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first is line integral, second...?... third ...?... .
Where I may find problems and how to solve 2nd and 3rd kind of ?
 
integral over a closed region in space PART OF USED FOR calculating volume or...?
 
LSE1234 said:
integral over a closed region in space PART OF USED FOR calculating volume or...?

The double integral with a circle over it is called a closed surface integral. It is commonly used to integrate a vector field defined over a closed surface (simply attach a vector to each point on the surface, this is a vector field. Ie., a head of hair or the flux of a fluid through a cross-section, or electromagnetic flux out of a sphere). If you instead integrate just the area form dA over the surface, you get the surface area.
Similarly, the triple integral with the circle over it integrates vector fields over closed volumes, but these are not as easily visualized.
The first courses where one may encounter extensive use of these objects are vector calculus and electrodynamics.
 
In CALCULUS II (undergraduate) these are get coveraged ?
 
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