Long description: block2fig4

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A graph illustrating the method of slicing, showing a thin, circular cross-section perpendicular to the x-axis for the curve defined by y equals x squared.

Alt text: A graph illustrating the method of slicing to find the volume of a solid of revolution, showing thin circular cross-sections.

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  • The image displays a two-dimensional Cartesian coordinate system with the horizontal axis labeled \(x\) and the vertical axis labeled \(y\), both marked with units.
  • A curve defined by the equation \(y = x^2\) is drawn, passing through the origin \((0, 0)\).
  • The region bounded by the \(x\)-axis and the curve \(y = x^2\) is shown. A representative point \((x, y)\) is marked on the curve.
  • A thin vertical rectangular strip, representing an infinitesimal slice of thickness \(\Delta x\), is drawn at the point \((x, y)\).
  • Perpendicular to the \(x\)-axis, a thin, shaded rectangular cross-section is shown at the point \((x, y)\). This cross-section is depicted as a thin circle (a disk) perpendicular to the \(x\)-axis.
  • Several instances of these thin, dashed and solid circular slices are drawn along the curve, illustrating the concept of slicing.
  • The graph is configured to show the volume generated by revolving the area under \(y = x^2\) around the \(x\)-axis, conceptually divided into these thin circular discs.

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