Key concepts 13.2-13.5

  • Definition of double integrals over bounded (begrensa) regions.
  • Fubini's theorem (iterated integrals) for double and triple integrals.
  • Elementary properties of double and triple integrals.
  • The area of a closed, bounded region \(R\) in the plane is \(A = \iint \limits_R \, dA\).
  • The volume of a closed, bounded region \(D\) in space is \(V = \iiint \limits_D \, dV\).
  • Average value (gjennomsnitt) of an integrable function over a bounded region in space and in the plane.
  • Definition of double integrals in polar coordinates.
  • The area of a closed, bounded region \(R\) in the plane is \(A = \iint \limits_R r \, dr \, d\theta\) in polar coordinates.
  • Change of an integral in Cartesian coordinates into one in polar coordinates.
  • Definition of triple integrals over bounded (begrensa) regions.
2013-03-05, erikmaki