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What is the difference between integration and anti-derivatives?
An integral and an anti-derivative are the same thing. Integration means the process of finding the integral, just as anti-differentiation means the process of finding the anti-derivative.
When adding numbers with fraction exponents do you add the exponents?
Fractional exponents follow the same rules as integral exponents. Integral exponents are numbers raised to an integer power.
Is the critical angle the same thing as the angle of incidence?
The critical angle is not the same thing as the angle of incidence. There is a reason the confusion. The critical angle is defined as the smallest angle of incidence which results in total internal reflection. Every plane wave incident on a flat surface has an angle of incidence. That can be any angle. When a wave travels from a dense medium to a less dense medium, there comes an angle of incidence where there is no transmission into the less dense medium. We say then that for an angle of incidence above the "critical angle" the result is total internal reflection. It is also true that with Snell's law, the critical angle is the particular angle of incidence which would result in a 90 degree angle of refraction.
How is Riemann- stieltjes integral a generalization of Riemann integral?
In reimann stieltjes integral if we assume a(x) = x then it becomes reimann integral so we can say R-S integral is generalized form of reimann integral.
Is integration a way of calculating the volume of the same function equation with an additional dimension or is it always completely new volume rotated about an axis ie a circle to a sphere?
Geometrically the definite integral from a to b is the area under the curve and the double integral is the volume under the surface. So just taking the integral of a function does not yield the volume of the solid made by rotating it around an axis. An integral is only a solid of revolution if you take an infinite sum of infinitesimally small cylinders that is the disk method or you do the same with shells.
