- #1
chetzread
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in part b , we can find mass by density x area ?
is it because of the thin plate, so, the thickness of plate can be ignored?
is it because of the thin plate, so, the thickness of plate can be ignored?
BvU said:There is no ignoring the thickness going on. The density function is a function of only two variables (*), so it provides mass/area, not mass/volume.
BvU said:There is no ignoring the thickness going on. The density function is a function of only two variables (*), so it provides mass/area, not mass/volume.
(*) as pointed out with the z=f(x,y) callout
(*) as pointed out with the z=f(x,y) callout
BvU said:There is no ignoring the thickness going on. The density function is a function of only two variables (*), so it provides mass/area, not mass/volume.
(*) as pointed out with the z=f(x,y) callout
so, z=f(x,y) provide info that density depends on 2 variables only?BvU said:There is no ignoring the thickness going on. The density function is a function of only two variables (*), so it provides mass/area, not mass/volume.
(*) as pointed out with the z=f(x,y) callout
A surface integral is a mathematical tool used to calculate the flux, or flow, of a vector field through a two-dimensional surface. It is a generalization of the concept of a line integral to higher dimensions.
A line integral is used to calculate the work done by a vector field along a one-dimensional curve, while a surface integral is used to calculate the flux of a vector field through a two-dimensional surface. In other words, a line integral deals with curves while a surface integral deals with surfaces.
Surface integrals have many real-world applications, including calculating the flow of air or water through a surface, calculating the heat flow through a surface, and calculating the electric or magnetic field through a surface.
The formula for a surface integral is ∫∫S F(x,y,z) · dS, where ∫∫S represents the surface integral, F(x,y,z) is a vector field, and dS is the differential element of surface area. This formula can be used to calculate the flux of a vector field through a surface.
There are two types of surface integrals: the flux integral, which calculates the flow of a vector field through a surface, and the surface area integral, which calculates the surface area of a three-dimensional object.