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Fundamental Theorem of Calculus definitions

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  • Definite Integral
    Represents the signed area under a curve between two bounds, calculated using antiderivatives and subtraction.
  • Antiderivative
    A function whose derivative returns the original function, used to evaluate definite integrals efficiently.
  • Continuity
    A property ensuring a function has no breaks or jumps on an interval, required for applying the theorem.
  • Interval
    A set of real numbers between two endpoints, often serving as the bounds for integration.
  • Upper Bound
    The highest value in the limits of integration, where the antiderivative is evaluated and subtracted.
  • Lower Bound
    The lowest value in the limits of integration, used as the starting point for evaluating the antiderivative.
  • Chain Rule
    A differentiation technique applied when the upper bound of an integral is a function of the variable.
  • Power Rule
    A method for finding antiderivatives or derivatives involving exponents, crucial for integration steps.
  • Variable Substitution
    The process of replacing the variable inside an integral with the upper bound during differentiation.
  • Signed Area
    The net area under a curve, accounting for regions above and below the x-axis, found using definite integrals.
  • Plus C
    The constant of integration, omitted in definite integrals since it cancels during subtraction of bounds.
  • Bar Notation
    A vertical line indicating evaluation of an antiderivative at the upper and lower bounds.
  • Function of x
    An expression where the variable x determines the output, often used as the upper bound in integrals.
  • Derivative
    A measure of how a function changes as its input changes, central to connecting integrals and antiderivatives.
  • Cancellation
    The phenomenon where differentiation and integration undo each other, yielding the original function.