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Introduction to Volume & Disk Method definitions

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  • Integral
    A mathematical tool used to sum infinitely many small quantities, such as areas or volumes, across a continuous interval.
  • Cross Section
    A two-dimensional shape revealed by slicing through a three-dimensional solid perpendicular to a chosen axis.
  • Area Function
    An expression representing the area of a cross section as a function of position, often used within an integral to find volume.
  • Solid of Revolution
    A three-dimensional object generated by rotating a plane curve around a fixed axis.
  • Disk Method
    A technique for finding volume by integrating the areas of circular cross sections perpendicular to the axis of revolution.
  • Radius Function
    A formula describing the distance from the axis of revolution to the curve, used as the radius in circular cross sections.
  • Axis of Revolution
    A fixed line around which a region or curve is rotated to create a three-dimensional solid.
  • Definite Integral
    An integral evaluated over specific bounds, yielding a numerical value such as area or volume.
  • Bounds
    The starting and ending values that define the interval over which an integral is calculated.
  • dx
    A symbol representing an infinitesimal width along the x-axis, used as the variable of integration.
  • dy
    A symbol representing an infinitesimal width along the y-axis, used as the variable of integration.
  • Function of x
    An expression where the variable x determines the output, often used to describe the base or height in volume problems.
  • Function of y
    An expression where the variable y determines the output, especially relevant when integrating with respect to y.
  • Interval
    A continuous range of values, typically defining the domain over which integration occurs.
  • πr²
    The formula for the area of a circle, used as the cross-sectional area in the disk method.