Lately I have been trying to learn the more intuitive/geometric meaning of integrals. I just have a copule of conceptual questions on different types of integrals and I would really appreciate it if someone would please help me.(adsbygoogle = window.adsbygoogle || []).push({});

OK, I know this so far:

[tex]\int_{I}f(x) dx[/tex]

[tex]\int\int_{R}f(x,y) dxdy[/tex]

[tex]\int\int\int_{R}f(x,yz) dxdydz[/tex]

The first two can be interpreted as the area and the volume under the function f(x) and f(x,y), respectively, and the third one can be interpreted as the total mass given that f(x,y,z) represents the mass per unit volume.

Now what about integrals such as line integrals ([tex]\int_{C}f(x) ds[/tex]), surface integrals ([tex]\int_{S}f(x,y) dS[/tex]) and volume integrals ([tex]\int_{V}f(x,y,z) dV$[/tex]? How do these differ from the other ones that I mentioned?

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# Line/surface/volume integrals

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