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since the line integral depends on the two values upper & lower limits and the function to which we have to integrate. the values changes only when the upper & lower limits changes, whatever the path is.
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What does path independence of line integral physically mean?
For a physical meaning, take potential energy as an example. To raise an object from one position to another position one meter higher takes a certain amount of energy - the potential energy of the object increases. The amount of energy is independent of the path the object takes - whether it goes straight up, in zigzag, etc.
What are Line integral Surface integral and Volume integral in simple words?
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
What is the shortest path between a line and a point not on that line?
The shortest path is a line perpendicular to the given line that passes through the given point.
What is the difference between a base path and a base line?
A base path is the path determined by the runner as he is travelling between bases, and the base line is the the direct lines between the two bases.
Is a straight path that goes on forever in two direction?
It is a straight line.
Discuss line integral and its real life applications?
A line integral can evaluate scalar and vector field functions along a curve/path. When applied on vector field, line integral is considered as measure of the total effect of the vector field along a specific curve whereas in scalar field application, the line integral is interpreted as the area under the field carved out by a particular curve.Line integral has many applications in physics. In mechanics, line integral is used to determine work done by a force in moving an object along a curve. In circuit analysis, it is used for calculating voltage.
What does path independence of line integral physically mean?
For a physical meaning, take potential energy as an example. To raise an object from one position to another position one meter higher takes a certain amount of energy - the potential energy of the object increases. The amount of energy is independent of the path the object takes - whether it goes straight up, in zigzag, etc.
Where will you use ampere circuital law in preference to biot savart law?
Ampere's circuital law is typically used to determine the magnetic field around symmetrically arranged current-carrying conductors or solenoids where the symmetry simplifies the calculation. On the other hand, the Biot-Savart law is employed for more general cases where the magnetic field needs to be calculated at any point in space due to a general current distribution. Ultimately, the choice between the two depends on the complexity of the current configuration and the ease of application of each method.
Line used to show the path of a wave?
A wave pulse is represented using a line in physics. This line shows the movement and propagation of the wave through a medium.
What is the Worlds hardest math equations?
Feynmans path integral formulation equations
How potential energy independent of path traveled?
It is independent of the path travelled. Its depend only on initial and final position and is a example of conservative force.
Which quantity is independent of the path taken?
Internal energy of a system is independent of the path taken, i.e., it only depends on the initial and final states of the system.
Is displacement or distance independent of path?
Distance is independent of path, as it is the total length traveled from point A to point B, regardless of the route taken. Displacement, on the other hand, is the shortest distance between the initial and final points and is also independent of path.
what path is created by moving points in space?
Orbital Pathway
What has the author D C Khandekar written?
D. C. Khandekar has written: 'Path-integral methods and their applications' -- subject(s): Path integrals, Feynman integrals
What are Line integral Surface integral and Volume integral in simple words?
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
What is the shortest path between a line and a point not on that line?
The shortest path is a line perpendicular to the given line that passes through the given point.
