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How do you derive the pi value using integral?
For example, by calculating the surface of a circle, using an integral.
What is the difference between definite integral and line integral?
Both kinds of integrals are essentially calculations of areas under curves. In a definite integral the surface whose area is to be calculated is planar. In a line integral the surface whose area to be calculated might occupy two or more dimensions. You might be interested in the animated diagrams in the wikipedia article for the line integral.
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 derivation of Coulomb's constant?
Coulomb's constant 'k' in the equation F=kQQ/r2 is derived from Gauss's law. Gauss's law stated that the charge enclosed by a theoretical surface is equal to the permittivity constant, represented by the Greek letter epsilon (because I can't use an epsilon, I will use an X) times the electric flux through the surface. Flux is equal to the closed integral of electric field vector dot the vector dA (infinitesimal change in surface area) of the surface. Becasue the surface surrounding one point charge is a perfect sphere, the dot product can be ignored (The surface is uniform and every change in area is normal to the electric field), and the Electric field is constant so it can be brought out of the integral leaving integral dA. When the integral is solved, the resulting equation is XEA=Q. A equals the surface area of the sphere so XE(4*pi*r2)=Q and E=Q/(4*pi*X*r2) and because F=EQ, F=QQ/(4*pi*X*r2). This is probably looking pretty familiar. All we have to do is make k=1/(4*pi*X) to make this equation equal to good old Coulomb's law. X, the permittivity constant equals 8.854*10-12 Farads per meter, or coulombs squared seconds squared per kilograms meters cubed. If you substitute this constant into the equation k=1/(4*pi*X), you obtain Coulmb's constant.
What structure does surface area represent in a cell?
plasma member
