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Indefinite Integrals definitions

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  • Indefinite Integral
    Reverse process of differentiation, represented by an elongated 's' symbol, always includes a constant of integration.
  • Antiderivative
    Function whose derivative yields the original function, found through integration.
  • Integrand
    Expression located inside the integral symbol, indicating what is being integrated.
  • Constant of Integration
    Arbitrary constant added to every indefinite integral, accounting for all possible antiderivatives.
  • Variable of Integration
    Symbol following 'd' in the integral, specifying the variable with respect to which integration occurs.
  • Power Rule
    Integration rule where the exponent increases by one and the result is divided by the new exponent.
  • Sum Rule
    Principle allowing the integral of a sum to be split into the sum of individual integrals.
  • Difference Rule
    Principle allowing the integral of a difference to be split into the difference of individual integrals.
  • Constant Multiple Rule
    Rule permitting a constant factor to be moved outside the integral for easier computation.
  • Polynomial
    Expression consisting of variables raised to whole number powers, often integrated term by term.
  • Notation
    System of symbols, such as the elongated 's' and 'dx', used to represent integration.
  • Derivative
    Operation that measures the rate of change of a function, reversed by integration.
  • Function
    Mathematical relationship where each input has a unique output, often the subject of integration.
  • Check
    Process of verifying an antiderivative by differentiating the result to recover the original integrand.