TRIPLE INTEGRALS
,Topics Covered
• Theory
• Meaning
• Rules for Solving
• Examples!
, Theory
As the name implies, triple integrals are 3 successive integrations,
used to calculate a volume, or to integrate in a 4th dimension,
over 3 other independent dimensions. Examples:
𝑉
𝑓 𝑥, 𝑦, 𝑧 𝑑𝑉
0
5 3𝑥−2 cos(𝑥+𝑦)
2𝑥 + 𝑒 𝑦𝑧 𝑑𝑧 𝑑𝑦 𝑑𝑥
1 0 sin(𝑥+𝑦)
2π 2 3
𝑟 𝑑𝑧 𝑑𝑟 𝑑𝜃
0 0 −3
,Topics Covered
• Theory
• Meaning
• Rules for Solving
• Examples!
, Theory
As the name implies, triple integrals are 3 successive integrations,
used to calculate a volume, or to integrate in a 4th dimension,
over 3 other independent dimensions. Examples:
𝑉
𝑓 𝑥, 𝑦, 𝑧 𝑑𝑉
0
5 3𝑥−2 cos(𝑥+𝑦)
2𝑥 + 𝑒 𝑦𝑧 𝑑𝑧 𝑑𝑦 𝑑𝑥
1 0 sin(𝑥+𝑦)
2π 2 3
𝑟 𝑑𝑧 𝑑𝑟 𝑑𝜃
0 0 −3
