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Консультация № 197072
13.11.2019, 18:38
0.00 руб.
15.11.2019, 15:38
0
1
1
Здравствуйте,
Вычислить
где область V ограничена плоскостями
x=0; y=0; z=2; z=6; x+y=4.
Вычислить
где область V ограничена плоскостями
x=0; y=0; z=2; z=6; x+y=4.
Обсуждение
23.11.2019, 15:14
общий
это ответ
Здравствуйте, mustang289!
Область V представляет собой треугольную призму, верхнее и нижнее основание которой лежат в плоскости z = 6 и z = 2 соответственно, а боковые грани - в плоскости x = 0, y = 0 и y = 4-x. Следовательно, интегрирование ведётся в пределах 0 [$8804$] x [$8804$] 4, 0 [$8804$] y [$8804$] 4-x, 2 [$8804$] z [$8804$] 6, и тройной интеграл сводится к повторному:
Область V представляет собой треугольную призму, верхнее и нижнее основание которой лежат в плоскости z = 6 и z = 2 соответственно, а боковые грани - в плоскости x = 0, y = 0 и y = 4-x. Следовательно, интегрирование ведётся в пределах 0 [$8804$] x [$8804$] 4, 0 [$8804$] y [$8804$] 4-x, 2 [$8804$] z [$8804$] 6, и тройной интеграл сводится к повторному:
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