Integral in simple words

Integrators begin to study integrals at school.

But none of the teachers say why it is necessary, how to use this knowledge in life. Few people are able to explain in simple words what integral is, even at university. And we will try.

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In short - integral, it is the sum of small parts. Yes, just like the addition of 2+2, only the parts are infinitely small, and naturally the number of them is infinite.The sign of the integral ∫ is an elongated letter s (the long "s" existed before the beginning of the 19th century, it was written this way - ſ). The first letter of the word summa.

Simple explanation

Why do you need it?

Examples from lifeIn simple words...

In short - integral, it is the sum of small parts. Yes, just like the addition of 2+2, only the parts are infinitely small, and naturally the number of them is infinite.The sign of the integral ∫ is an elongated letter s (the long "s" existed before the beginning of the 19th century, it was written this way - ſ). The first letter of the word summa.

definite integral calculator

Integration is the addition of an infinite number of parts of infinitely small meaning.Why is the usual "plus" not enough? There are simply no infinitely small or large parts in algebra.An infinitely small value is not a specific number. It is an abstraction; there are simply no analogues in the real world. We invented it for convenience. Something so small that it makes no sense to measure it, but you can use it in your calculations.The word "integral" comes from the Latin integer, which means "whole". Even the name has a hint of some kind of action, something like restoring something whole.

It is best to show "on your fingers", or rather by example. Suppose we want to know the area of the figure as in the picture (it's called a curvilinear trapeze because one of the sides is created by a curved line). Why do we need it? For example, it is a part of an airplane wing and we want to know its area.Available explanation of the integralYou can, of course, split a figure into two, a rectangle and a triangle.Just an integral.But there will remain a "gap", the area of which will be unknown. To increase accuracy, you can divide it into more figures, but still there will be some area, albeit small, but "not painted". The shapes will become smaller and smaller... Obviously, the grinding process will be infinite, at least in the imagination.But, in reality, an infinite process is simply not needed. In fact, it is impossible to calculate such things as the area of the circle, the length of the diagonal of the square or the volume of the pyramid, the value will be infinite, of course, practical sense infinite numbers do not have and we "round them up" to the desired accuracy limit - approximately.

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definite integral calculator

Integration is the addition of an infinite number of parts of infinitely small meaning.Why is the usual "plus" not enough? There are simply no infinitely small or large parts in algebra.An infinitely small value is not a specific number. It is an abstraction; there are simply no analogues in the real world. We invented it for convenience. Something so small that it makes no sense to measure it, but you can use it in your calculations.The word "integral" comes from the Latin integer, which means "whole". Even the name has a hint of some kind of action, something like restoring something whole.

It is best to show "on your fingers", or rather by example. Suppose we want to know the area of the figure as in the picture (it's called a curvilinear trapeze because one of the sides is created by a curved line). Why do we need it? For example, it is a part of an airplane wing and we want to know its area.Available explanation of the integralYou can, of course, split a figure into two, a rectangle and a triangle.Just an integral.But there will remain a "gap", the area of which will be unknown. To increase accuracy, you can divide it into more figures, but still there will be some area, albeit small, but "not painted". The shapes will become smaller and smaller... Obviously, the grinding process will be infinite, at least in the imagination.But, in reality, an infinite process is simply not needed. In fact, it is impossible to calculate such things as the area of the circle, the length of the diagonal of the square or the volume of the pyramid, the value will be infinite, of course, practical sense infinite numbers do not have and we "round them up" to the desired accuracy limit - approximately.

Cool Math Games

Cheap Essay Writer