Math Insight

Pages similar to: Length of curves

• 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.
• 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.
• Volumes by cross sections
  Calculating the volume of a solid by integrating the area of its cross sections.
• Volume of surfaces of revolution
  Calculating the volume of created by rotating a plane region around some axis.
• 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.
• The arc length of a parametrized curve
  Introduction to the arc length of a parametrized curve. The arc length definition is illustrated with interactive graphics.
• Introduction to a line integral of a scalar-valued function
  Introduction with interactive graphics illustrating the line integral of a scalar-valued function and informally deriving the formula for calculating the integral from the parametrization of the curve.
• Line integrals are independent of parametrization
  Description of how the value of a line integral over a curve is independent of the parametrization of the curve.
• Examples of scalar line integrals
  Examples demonstrating how to calculate line integrals of scalar-valued functions.
• Introduction to a line integral of a vector field
  The concepts behind the line integral of a vector field along a curve are illustrated by interactive graphics representing the work done on a magnetic particle. The graphics motivate the formula for the line integral.
• Integrating Taylor polynomials: first example
  An example showing how to integrate a Taylor polynomial and interpret the result.

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