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The process of continuously summing changes in a function f(x). It is the basis of the integral calculus and the opposite process to differentiation. The function to be integrated is called the integrand and the result of integration on the integrand is called the integral. For example, the integration of f(x) is written ∫f(x)dx, the differential dx being added to indicate that f(x) must be integrated with respect to x. To complete the integration, a constant of integration, C, must be added where no interval over which the integration takes place is given. This is called an indefinite integral. If the interval is specified, e.g.∫abf(x)dx,no constant of integration is required and the result is called a definite integral. This means that f(x) is to be integrated between the values x = a and x = b to give a definite value.

Subjects: Mathematics.

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