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Area Between Curves definitions

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  • Definite Integral
    A calculation that finds the net area under a curve between two specific bounds on the x-axis.
  • Intersection Point
    A location where two functions have equal values, often used to determine the limits of integration.
  • Bound
    A value that marks the start or end of an interval over which an integral is evaluated.
  • Top Function
    The curve that lies above another within a given interval, used as the minuend in area calculations.
  • Bottom Function
    The curve that lies below another within a given interval, used as the subtrahend in area calculations.
  • Interval
    A continuous range of x-values over which area calculations or integrations are performed.
  • Integrand
    The expression inside an integral sign, representing the function to be integrated.
  • Power Rule
    A method for finding antiderivatives, where the exponent is increased by one and divided by the new exponent.
  • Antiderivative
    A function whose derivative yields the original integrand, used to evaluate definite integrals.
  • Fundamental Theorem of Calculus
    A principle connecting differentiation and integration, allowing evaluation of definite integrals using antiderivatives.
  • Quadratic Equation
    An equation of degree two, often solved to find intersection points between curves.
  • Factoring
    An algebraic process to rewrite a quadratic equation as a product of linear terms, aiding in finding roots.
  • Standard Form
    An arrangement of a polynomial with terms ordered by descending powers of the variable.
  • Area Between Curves
    A region bounded vertically by two functions, calculated by integrating the difference of their values.
  • Switching Functions
    A scenario where the roles of top and bottom functions change within an interval, requiring split integrals.