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Improper Integrals definitions

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  • Improper Integral
    A definite integral with at least one infinite bound, requiring limits to evaluate.
  • Infinite Bound
    A situation where the lower or upper limit of integration extends to positive or negative infinity.
  • Limit
    A mathematical process used to define values as a variable approaches infinity or negative infinity.
  • Convergence
    A condition where the evaluated limit of an improper integral results in a finite value.
  • Divergence
    A condition where the evaluated limit of an improper integral does not result in a finite value.
  • Upper Bound
    The highest value in the interval of integration, which can be infinity in improper integrals.
  • Lower Bound
    The lowest value in the interval of integration, which can be negative infinity in improper integrals.
  • Continuous Function
    A function with no breaks or jumps, allowing integration over infinite intervals.
  • Area Under the Curve
    The region between a function and the x-axis, extended to infinity in improper integrals.
  • Definite Integral
    An integral evaluated between two specific bounds, possibly infinite in improper cases.
  • Variable Substitution
    The process of replacing infinity with a variable, then applying a limit as the variable approaches infinity.
  • Finite Number
    A real, non-infinite value resulting from a convergent improper integral.
  • Splitting Integrals
    Dividing an integral with both bounds infinite into two parts at a constant for evaluation.
  • Exponent
    A mathematical expression indicating repeated multiplication, crucial in evaluating functions like e^x at infinity.
  • Constant
    A fixed value used to separate or define intervals when splitting improper integrals.