The triple integral. Properties of triple integrals. The calculation of the triple integral and volumes of solids презентация

Слайд 2

If f (x; y; z)> 0 on U, the mass M

If f (x; y; z)> 0 on U, the mass M of the
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 3

EVIDENCE

Since f (x; y; z) = I> 0 to Y, then

-

EVIDENCE Since f (x; y; z) = I> 0 to Y, then -
Body weight at a density of γ = 1.
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 4

6. 

If you know the smallest and the largest M m values

6. If you know the smallest and the largest M m values of
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.

Имя файла: The-triple-integral.-Properties-of-triple-integrals.-The-calculation-of-the-triple-integral-and-volumes-of-solids.pptx
Количество просмотров: 97
Количество скачиваний: 0