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coverband
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When calculating surface integrals do you have to calculate double integrals for dxdy, dxdz and dydz and add up or what?
Defennder said:If you use any 2 of the three variables x,y,z then you have to set up the double integrals with respect to them.
coverband said:But this is sufficient? If you integrate say with respect to dxdy and have correct and appropriate limits then this is the question answered so to speak. You don't have to go on and do dxdz and dydz?
coverband said:I appreciate the attention but is the answer to do you just integrate with respect to dxdy in all cases yes !?
coverband said:Thanks no more exams. So say if you have surface z=x+y+1 then you integrate with respect to dxdy and that's it finished problem solved
If you have x=z-y-1 then you integrate with respect to dzdy and that's it finished
You don't do all three and add them up or anything !?
nsama said:for the question i posted, the x² is a power of e. thanx.
A surface integral is a type of integral that is used to calculate the area of a surface or the volume bounded by a surface in three-dimensional space.
There are three types of surface integrals: double integrals, triple integrals, and line integrals. Double integrals are used to calculate the area of a surface, triple integrals are used to calculate the volume bounded by a surface, and line integrals are used to calculate the work done by a force field along a curve on a surface.
To calculate a surface integral using dxdy, dxdz, or dydz, you first need to parameterize the surface in terms of two variables. Then, you can use the appropriate integral to calculate the area or volume of the surface.
A closed surface is a surface that completely encloses a volume, while an open surface does not enclose a volume and has a boundary. Closed surfaces are typically used for calculating triple integrals, while open surfaces are used for calculating double integrals.
Surface integrals have many applications in physics and engineering. They can be used to calculate the flux of a vector field through a surface, the mass of a three-dimensional object, and the work done by a force field on a surface. They are also used in fields such as fluid dynamics, electromagnetism, and thermodynamics.