What is the physical significance of double and triple integrals?
My book says double integral and triple integral gives mass of body in two dimensional and three dimensional space respectively.
Sites on internet say it different like double integral gives volume.
Are these two different applications of double and triple integral? Or something else? And what actually are double and triple integral, like we have to provide definition then?
Best Answer
Double integrals, in general, is when you integrate over any two variables, and with triple integrals, you integrate over any three variables.
But often in physics, these two or three variables represent space. Two spatial variables multiplied together gives something with the unit of an area and three gives something with the unit of volume.
So if you for instance integrated a density (with units mass per volume) three times over space, you'd get something with the unit of just mass. If you, alternatively, integrated a density that was defined in terms of mass per area two times, you'd also get a mass in the end.