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Консультация № 196944
03.11.2019, 20:56
0.00 руб.
05.11.2019, 07:27
0
2
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить тройной интеграл в сферических координатах: ∫∫∫√(x^2 + y^2 + z^2) dxdydz, где V : x^2 + y^2 + z^2 = 16; y ≥ 0, z ≥ 0, y ≥ x .
^ - степень.
Вычислить тройной интеграл в сферических координатах: ∫∫∫√(x^2 + y^2 + z^2) dxdydz, где V : x^2 + y^2 + z^2 = 16; y ≥ 0, z ≥ 0, y ≥ x .
^ - степень.
Обсуждение
08.11.2019, 19:16
общий
это ответ
Здравствуйте, mark.martynenko.99!
Переход к сферическим координатам осуществляется по формулам x = r sin [$952$] cos [$966$], y = r sin [$952$] sin [$966$], z=r cos [$952$]. Тогда dx dy dz = r[sup]2[/sup]sin [$952$] dr d[$952$] d[$966$], подинтегральное выражение будет равно r, а уравнения поверхностей примут вид r[sup]2[/sup] = 16, r sin [$952$] sin [$966$] [$8805$] 0, r cos [$952$] [$8805$] 0, r sin [$952$] sin [$966$] [$8805$] r cos [$952$] sin [$966$], то есть пределами интегрирования будут 0 [$8804$] r [$8804$] 4, 0 [$8804$] [$952$] [$8804$] [$960$]/2, [$960$]/4 [$8804$] [$966$] [$8804$] [$960$]. Интеграл будет равен
Переход к сферическим координатам осуществляется по формулам x = r sin [$952$] cos [$966$], y = r sin [$952$] sin [$966$], z=r cos [$952$]. Тогда dx dy dz = r[sup]2[/sup]sin [$952$] dr d[$952$] d[$966$], подинтегральное выражение будет равно r, а уравнения поверхностей примут вид r[sup]2[/sup] = 16, r sin [$952$] sin [$966$] [$8805$] 0, r cos [$952$] [$8805$] 0, r sin [$952$] sin [$966$] [$8805$] r cos [$952$] sin [$966$], то есть пределами интегрирования будут 0 [$8804$] r [$8804$] 4, 0 [$8804$] [$952$] [$8804$] [$960$]/2, [$960$]/4 [$8804$] [$966$] [$8804$] [$960$]. Интеграл будет равен
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