Integration
is an important concept of Mathematics. It is one of the two calculus other
than differentiation.
Integration is a method of adding discrete data, especially in large scale industries.
While on a small scale, we can easily add the quantities by simple calculations, but for sectors which have discrete data, it is not easy to do the calculations.
Integrals are used to determine many useful quantities, such as areas, volumes, displacement, etc.
Integration is a method of adding discrete data, especially in large scale industries.
While on a small scale, we can easily add the quantities by simple calculations, but for sectors which have discrete data, it is not easy to do the calculations.
Integrals are used to determine many useful quantities, such as areas, volumes, displacement, etc.
Integration
is the process to figure out the cumulative impact of forces that experience
variations as they work on a body while it is in motion. Integrals allow us to
define the collective effect of kinetic energy.
In
a widespread, the concept of limit is used in calculus, where algebra and
geometry are implemented. Limits help us in the study of the result of points
on a graph such as how they get closer to each other until their distance is
almost zero. We would learn here two types of integrals. They are definite integral and indefinite integral.
An
integral that includes the upper and lower limits is said to be a definite
integral, whereas indefinite integrals are defined without upper and lower
limits. But, why do we need to calculate the integrals? What are the
applications of integrals? The answer to these questions are:
● To find the area between the curves
● To find the distance, velocity and acceleration
● To find the volume
● To find the work done
● To find the kinetic energy
● To find the probability
● To find the average value of a function
● To find the surface area
Now
how do we calculate these quantities using integrals? So, there are two methods
by which integration can be done, i.e., either by substitution or by parts.
In
the substitution method, either of the given integral is
transformed into a simple form by substituting the independent variable by
others. In calculus, the substitution method is also termed as the “Reverse
Chain Rule” or “U-Substitution Method”. Integration by parts is a unique technique of combination of two functions
when they are multiplied with each other. This method is also called partial
integration.
Integration
is the usual method to find complete change when you know tiny changes. The
term "Integrate" is a Latin word and it means "make whole".
Integration in Other Subjects
In
Chemistry, integration is beneficial. Chemical kinetics use the rate of change
of concentration of several species. Upon integrating, we get the relationship
between mass and time. Integration is also used to determine some formulae of
thermodynamics.
Integration
is widely used in Physics, as well. Gauss's law for electrostatics, Ampere's
law for magnetism, Maxwell's equations, all of them use integration. Many
physical queries involving mechanics, electromagnetism, atomic and nuclear
phenomena, etc. can be easily answered using integration.
