Integration के रहस्य the invention which changed the mathematics

Integration is a way of uniting the part to find a whole. In the integral calculus, we find a function whose differential is given. Thus integration is the inverse of differentiation. Integration is used to define and calculate the area of the region bounded by the graph of functions. The area of the curved shape is approximated by tracing the number of sides of the polygon inscribed in it. This process known as the method of exhaustion was later adopted as integration. We obtain two forms of integrals, indefinite and definite integrals. Differentiation and integration are the fundamental tools in calculus that are used to solve problems in math and physics. The principles of integration were formulated by Leibniz. Let's move further and learn about integration, its properties, and some of its powerful techniques.
Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration.
If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) +C. These are indefinite integrals. For example, let f(x) = x3 be a function. The derivative of f(x) is f’(x) = 3x2 and the antiderivative of 3x2 is f(x) = x3
We are given a derivative of a function and are asked to find its primitive, that is, the original function. Such a process is called anti-differentiation or integration. If we are given the derivative of a function, the process of finding the original function is called integration. The derivatives and the integrals are opposite to each other. Consider a function f(x)= sin x. The derivative of f(x) is f'(x) = cos x. We say that the function cos x is the derived function of sin x. Similarly, we say that sin x is the anti-derivative of cos x.

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Integration के रहस्य the invention which changed the mathematics

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