The triple integral. Properties of triple integrals. The calculation of the triple integral and volumes of solids презентация
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- The triple integral. Properties of triple integrals. The calculation of the triple integral and volumes of solids
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Слайд 2If f (x; y; z)> 0 on U, the mass M
If f (x; y; z)> 0 on U, the mass M
of the body variable density γ = f (x; y; z) is calculated using the formula:
2. The volume of the body
1. The physical meaning of the triple integral
Слайд 3EVIDENCE
Since f (x; y; z) = I> 0 to Y, then
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EVIDENCE
Since f (x; y; z) = I> 0 to Y, then
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Body weight at a density of γ = 1.
Therefore, M = γ · V = 1 · V = V. As a result, I = V, as required.
Therefore, M = γ · V = 1 · V = V. As a result, I = V, as required.
3.
4.
If U = U1 U2, where U1 and U2 do not intersect,
5.
Слайд 46.
If you know the smallest and the largest M m values
6.
If you know the smallest and the largest M m values
of a continuous function f (x; y; z), (x; y; z) isin U in U, then the triple integral is estimated as follows:
7.
Theorem 2.6 (the mean value of the double integral):
where M * - a kind of "average" point of the domain U, f (x; y; z) - continuous in U.
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