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A line integral is a simple integral.
they look like:
integral x=a to b of (f(x)).
A surface integral is an integral of two variables.
they look like:
integral x=a to b, y=c to d of (f(x,y)).
or
integral x=a to b of (integral y=c to d of (f(x,y))).
The second form is the nested form. A pair of line integrals, one inside the other. This is the easiest way to understand surface integrals, and, normally, solve surface integrals.
A volume integral is an integral of three variables.
they look like:
integral x=a to b, y=c to d, z=e to f of (f(x,y,z)).
or
integral x=a to b of (integral y=c to d of (integral z=e to f of f(x,y,z))).
the above statement is wrong, the person who wrote this stated the first 2 types of integrals as regular, simple, scalar integrals, when line and surface integrals are actually a form of vector calculus. in the previous answer, it is stated that the integrand is just some funtion of x when it is actually usually a vector field and instead of evaluating the integral from some x a to b, you will actually be evaluating the integral along a curve that you will parametrize to get the upper and lower bounds of the integral. as you can see, these are a lot more complicated.
looking at your question tho, i dont think you want the whole expanation on how to solve these problems, but more so what they are and what they are used for, because these can be a pain to solve and there are also several ways to solve them indirectly.
line integrals have an important part in physics because they alow us to calculate things such as work that have vector values rather than just scalar values as you can use these integrals to describe a particles path along a curve in a force field. surface integrals help us calculate things like flux, or how fluid flows over a surface.
if you want to learn more, look into things like greens theorem, or the divergence theorem.
p.s. his definition of a surface integral is acutally how you find the volume of a region
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What are some related words for surface area of a cylinder?
face or surface are related words for a surface area of a cylinder
How can we find the volume of a2d geometrical figure arhtematically?
I am not sure I can navigate through the typographic disaster zone here but it appears as if the question concerns finding the volume of a 2-dimensional geometric figure.If so, the answer is very simple: the volume is zero. By definition, 2-d figures can have lengths and areas but, since they do not have a third dimension, they cannot have a volume. In other words, VOLUME = 0.
Can a simple predicate be two words?
yes it can example: can fly that is a simple predicate
Simple words that start with x?
Xylophone
What are 3 short a vowel words?
Simple short A words are apple, hat, and back.
What 3D shape has the most surface area?
For a given volume, you can make the surface area arbitrarily large. In other words, there is no upper limit.
When the volume of a cell increases its surface area?
increases: by approximately the square of the cube root of the volume increase (that would be exact if the cell was a sphere). Or, in other words, if you double the size (diameter) of a cell. its surface area increases by a factor of 4, and it volume increases by a factor of 8.
What is definition of volume in simple words?
Volume may be the 'loudness' of a sound. It may also mean the amount of substance a container may hold or how much space an object occupies.
What are some related words for surface area of a cylinder?
face or surface are related words for a surface area of a cylinder
What words can you make out of the word simple?
Some words that can be made from 'simple' are:elmII'mimpmemilepiepileslimslimeslipsmile
Is Stephenie Meyer's words simple or fancy?
Her words are mostly simple but through those simple words she creates such beautiful imaginations in the minds of the readers which you cannot do with elaborate words.
How can we find the volume of a2d geometrical figure arhtematically?
I am not sure I can navigate through the typographic disaster zone here but it appears as if the question concerns finding the volume of a 2-dimensional geometric figure.If so, the answer is very simple: the volume is zero. By definition, 2-d figures can have lengths and areas but, since they do not have a third dimension, they cannot have a volume. In other words, VOLUME = 0.
Can someone explain the meaning of condensation with very simple words?
Condensation is when water turns from a gas or suspended liquid in the air to a liquid on a surface because it cooled down.
What are some math words that begin with the letter I?
Yes e.g. Indices, Integer, Integrateinteger, integral, and inverse
What is flux inegral?
A flux integral is the summation of the component of a vector field perpendicular to differential surface areas (or in the direction of their normal vectors) over the entire surface. In other words, the flux of a vector field across a surface is the surface integral vector field in the direction of the normal component of the surface.INT INTS[(F*n)dS]INT INT is the double integral operatorS is the surface domain being integrated overF is a vector field* is the dot productn is the normal component to the surfacedS is the differential surface area.Flux integrals are very useful in physics. Two of Maxwell's equations involve flux integrals:INT INTS[(B*n)dS] = 0This equation states that the magnetic flux over a closed surface is always equal to zero. This equation reflects the fact that magnetic monopoles do not exist.INT INTS[(E*n)dS] = Q/EThis equation states that the electric flux through a closed surface is proportional to the total charge enclosed within that surface (1/E is the proportionality constant). These equations played important roles in the discovery of electromagnetic radiation.also the Flux of a velocity field through a surface indicates the flow rate across that surface.
What is the word that start with integ?
Intangible, integer, integral, integrate, integration and integrity are words. They begin with the letters INTEG.
How do you keep the volume of an object the same but change the surface area?
Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.Increase the magnitude of one dimension while reducing the other two. In other words, make the shape thin and flat but very long.For example, a 4*4*4 cube has a volume of 64 cubic units and a surface area of 96 square units.A 1*1*64 cuboid, on the other hand, has the same volume but its surface area is 258 square units.Similarly, starting from a sphere, the volume can be maintained but the surface area increased by making it a very thin, flat but long ellipsoid.In mathematical terms there is no limit to how thin or flat, nor how long the shape can be and so there is no limit to the surface area. In real life, of course, no dimension can be made smaller than a molecule and even that is doubtful.
