Integration Quiz

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Definition

In calculus, integration is the inverse or reverse of differentiation. It is an addition to the theory of summation. Integration is heavily used in many calculations in calculus. When combined with differentiation, it becomes a very useful and powerful concept used to solve and compute a large variety of mathematical problems.

Uses

  • Integration can be used to find:
  • » The area underneath a curve
  • » The displacement of a moving object.
  • » The centroid of an area with curved surfaces which is also similar to the centre of a mass of a body.
  • » Integrals of stochastic processes in finance.
  • » Laplace transforms.
  • » Fourier transforms.

Types of integral equations

  • » Integration by substitution.
  • » Integration by parts.
  • » Linear integral equations.
  • » Volterra integral equations of the first kind.
  • » Volterra integral equations of the second kind.
  • » Fredholm integral equations of the first kind.
  • » Fredholm integral equations of the second kind.
  • » Integral equations with variable limits of integration.
  • » Integral equations with constant limits of integration.