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Lecture on Multiple Integrals
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  • Course
  • Mathematics (KNF2033)
  • Institution
  • UNIMAS

The lecture note covers: i)Area of a Region, Volume of a Solid, Centroid and Moment of Inertia, Green’s Theorem ii) Coordinate system iii) Jacobian iv) Surface integrals v) Triple integrals, vi) Divergence theorem

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  • August 26, 2021
  • 103
  • 2021/2022
  • Class notes
  • Hazrul mohamed basri
  • All classes

Subjects

  • double integrals
  • green’s theorem

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  • UNIMAS
  • Mathematics (KNF2033)
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DOUBLE INTEGRALS AND GREEN’S THEOREM IN A PLANE

, Area of a Volume of a
DOUBLE INTEGRALS Region Solid
AND GREEN’S
THEOREM IN A PLANE Presentation
outlines
LEARNING UNIT 3 Centroid and
Green’s
Moment of
Theorem
Inertia

, DOUBLE INTEGRATION
• In a double integral we integrate a
function 𝑓(𝑥, 𝑦) , called the
integrand, over a closed bounded
region ℛ 2 in the 𝑥𝑦 −plane, whose
boundary curve has a unique
tangent at each point.
• double integral of f(x, y) over the
region ℛ, and is denoted by


ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 𝑜𝑟 ඵ 𝑓 𝑥, 𝑦 𝑑𝐴
ℛ ℛ

, PROPERTIES OF DOUBLE INTEGRALS

ඵ 𝑘 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 = 𝑘 ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 , 𝑘 𝑖𝑠 𝑎 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
ℛ ℛ



ඵ 𝑓 𝑥, 𝑦 + 𝑔(𝑥, 𝑦) 𝑑𝑥𝑑𝑦 = ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 + ඵ 𝑔 𝑥, 𝑦 𝑑𝑥𝑑𝑦
ℛ ℛ ℛ



ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 = ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦 + ඵ 𝑓 𝑥, 𝑦 𝑑𝑥𝑑𝑦
ℛ1 +ℛ2 ℛ1 ℛ2

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