Integration Class 12 Solutions|NEB| mathematics|

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an antiderivative, also known as an indefinite integral, is a function that when differentiated, produces a given function as its result. in other words, it is the reverse operation of differentiation.

for example, if we have a function f(x), its antiderivative f(x) can be written as:

f(x) = ∫ f(x) dx

here, the symbol "∫" represents the integral sign and dx represents the variable of integration. the antiderivative is denoted by a capital "f" to distinguish it from the original function f(x).

the antiderivative is not unique, as adding a constant of integration (c) to the function does not change its derivative. this constant represents the family of all possible antiderivatives of a given function.

the process of finding antiderivatives is known as integration. there are several methods of integration, including substitution, integration by parts, and trigonometric substitution, among others. these methods involve various techniques to transform the integrand into a form that can be integrated.

the concept of antiderivatives is essential in calculus, as it provides a way to calculate the area under a curve, which is represented by the definite integral. the fundamental theorem of calculus establishes a relationship between the definite integral and the antiderivative of a function. it states that the definite integral of a function f(x) between two points a and b is equal to the difference between its antiderivative evaluated at b and a:

∫ (a to b) f(x) dx = f(b) - f(a)

Here, you can find the complete Solution of integration Chapter in PDF design. You can see every one of the arrangements in the PDF implant beneath.If you want old is gold question bank for class 12 then click the highlights underlined parts.

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