PROPERTIES OF LINE INTEGRALS

Pocket

Line integrals have properties which are analogous to those of ordinary integrals. For example:

  1. \displaystyle \int_C [P(x, y)dx + Q(x, y)dy] = \int_C P(x, y)dx + \int_C Q(x, y)dy
  2. \displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = - \int_{(a_2, b_2)}^{(a_1, b_1)}[Pdx + Qdy]
  3. Thus reversal of the path of integration changes the sign of the line integral.

  4. \displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = \int_{(a_1, b_1)}^{(a_3, b_3)} [Pdx + Qdy] + \int_{(a_3, b_3)}^{(a_2, b_2)} [Pdx + Qdy]
  5. where (a_3, b_3) is another point on C.

Similar properties hold for line integrals in space.

Pocket

投稿者: admin

趣味:写真撮影とデータベース. カメラ:TOYO FIELD, Hasselblad 500C/M, Leica M6. SQL Server 2008 R2, MySQL, Microsoft Access.

コメントを残す

メールアドレスが公開されることはありません。 が付いている欄は必須項目です