Math Insight

Pages similar to: Volume of surfaces of revolution

• Volumes by cross sections
  Calculating the volume of a solid by integrating the area of its cross sections.
• Basic integration formulas
  Formulas for integration based on reversing formulas for differentiation.
• The simplest integration substitutions
  Reversing a simple chain rule application to compute integrals.
• Integration substitutions
  Reversing the chain rule to compute integrals.
• Area and definite integrals
  Integrating to find the area under a curve or the area between two curves.
• Length of curves
  An integral to find the length of a curve.
• Numerical integration
  Methods to approximate the value of definite integrals and estimate the error in the approximations.
• Averages and weighted averages
  Using integrals to calculate averages and weighted averages of a function.
• Centers of mass (centroids)
  An integral to find the length of a curve.
• Integration by parts
  Using the product rule backwards to simplify integrals.
• Partial fractions
  Using algebra to simplify the integral of rational functions.
• Trigonometric integrals
  Using trigonometric identities to calculate integrals involving trigonometric functions.
• Trigonometric substitution
  Using trigonometric substitution to simplify integrals involving square roots.
• Developing intuition about the indefinite integral
  An intuitive exploration into the properties of the indefinite integral, illustrated by interactive graphics.
• Double integrals as volume
  Explanation of how double integrals could be used to represent volume.
• Integrating Taylor polynomials: first example
  An example showing how to integrate a Taylor polynomial and interpret the result.
• Integrating the error term of a Taylor polynomial: example
  An example showing how to integrate the error term of Taylor polynomial and interpret the result.
• Volume calculation for changing variables in triple integrals
  A derivation of how a mapping that changes variables in triple integrals transforms volume.
• Using the Forward Euler algorithm to solve pure-time differential equations
  By pretending that the slope of a function is constant over small intervals, we following tangent lines to estimate the solution to pure-time differential equations.
• Elementary integral problems
  Sample problems illustrating the indefinite and definite integral.

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