Question

please please please please dear answer I have exam
I want mathematical essence of integral with examples
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Answer 1

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Actually Welcome to the Concept of the Integral Calculus.

Basically if we see the, The whole world is based on two things that is bonding and breaking.

This bonding and breaking in mathematics can be so called as the Newton's Calculus.

If we look at any expression that can a, linear, planer or a three dimensional figure, we can easily find it's area, volume or it's tangent and asymptodes ( tangents at infinity) , by applying the Differential and Integral calculus.

Looking deeply at the Integration, it is the reverse process of the differentiation.

The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the x-axis. The technical definition of the definite integral involves the limit of a sum of areas of rectangles.

The symbol of integration is an elongated S (the S stands for "sum"). The definite integral is written as:

The indefinite integral, or antiderivative, is written:

Functions differing by only a constant have the same derivative, and it can be shown that the antiderivative of a given function is actually a family of functions differing only by a constant. Since the derivative of the function y = x2 + C, where C is any constant, is y′ = 2x, the antiderivative of the latter is given by:

Some of the formulae for the Integration are as.

1.) dy/dx = nx, y = x^n+1/n+1 + C

2.) dy/dx = sinx, y = -cos x + C

and so on...