# I saw somewhere triple line integrals

1. Aug 28, 2009

### LSE1234

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 ?

2. Aug 29, 2009

### HallsofIvy

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.

$\skew{57} {\skew{15}\subset \supset} \iiint dV\mbox{ }$ 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.

Last edited by a moderator: Aug 29, 2009
3. Aug 29, 2009

### LSE1234

first is line integral, second....?.... third ....?.... .
Where I may find problems and how to solve 2nd and 3rd kind of ?

4. Aug 29, 2009

### LSE1234

integral over a closed region in space PART OF USED FOR calculating volume or...?

5. Aug 29, 2009

### slider142

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.

6. Aug 29, 2009

### LSE1234

In CALCULUS II (undergraduate) these are get coveraged ?