Файл: Учебное пособие предисловие данное учебное пособие предназначено для студентов немате.docx

, вы- числить интеграл, если область интегрирования (V ) ограничена по- верхностями, заданными уравнениями.

№	Интеграл	Область интегрирования (V)
1	,,, √x2+y2dxdydz (V)	x2 + y2 = 2x, z= x2 + y2, z= 0 при x2 + y2 ≤ 2x
2	,,, √x2+y2dxdydz (V)	x2 + y2 = 2x, x2 + y2 + z= 0, z= −4 при x2 + y2 ≤ 2x
3	,,, √x2+y2dxdydz (V)	x2 + y2 = −2x, z= x2 + y2, z= 0 при x2 + y2 ≤ −2x
4	,,, √x2+y2dxdydz (V)	x2 + y2 = −2x, x2 + y2 + z= 0, z= −4 при x2 + y2 ≤ −2x
5	,,, √x2+y2dxdydz (V)	x2 + y2 = 2y, z= x2 + y2, z= 0 при x2 + y2 ≤ 2y
6	,,, √x2+y2dxdydz (V)	x2 + y2 = 2y, x2 + y2 + z= 0, z= −4 при x2 + y2 ≤ 2y
7	,,, √x2+y2dxdydz (V)	x2 + y2 + 2y= 0, z= x2 + y2, z= 0 при x2 + y2 ≤ −2y
8	,,, √x2+y2dxdydz (V)	x2 + y2 + 2y= 0, x2 + y2 + z= 0, z= −4 при x2 + y2 ≤ −2y
9	,,, √x2+y2dxdydz (V)	x2 + y2 = 2x, 4 − z= x2 + y2, z= 4 при x2 + y2 ≤ 2x
10	,,, √x2 + y2dxdydz (V)	x2 + y2 = 2x, z− 4 = x2 + y2, z= 0 при x2 + y2 ≤ 2x

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11	,,, √x2+y2dxdydz (V)	x2 + y2 = −2x, 4 − z= x2 + y2, z= 4 при x2 + y2 ≤ −2x
12	,,, √x2+y2dxdydz (V)	x2 + y2 = −2x, z− 4 = x2 + y2, z= 0 при x2 + y2 ≤ −2x
13	,,, √x2+y2dxdydz (V)	x2 + y2 = 2y, 4 − z= x2 + y2, z= 4 при x2 + y2 ≤ 2y
14	,,, √x2+y2dxdydz (V)	x2 + y2 = 2y, z− 4 = x2 + y2, z= 0 при x2 + y2 ≤ 2y
15	,,, √x2+y2dxdydz (V)	x2 + y2 + 2y= 0, 4 − z= x2 + y2, z= 4 при x2 + y2 ≤ −2y
16	,,, √x2 + y2dxdydz (V)	x2 + y2 + 2y= 0, z− 4 = x2 + y2, z= 0 при x2 + y2 ≤ −2y
17	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(x2 − y2), 2z= x2 + y2, z= 0, если 0 ≤ x
18	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(x2 − y2), 2z= x2 + y2, z= 0, если 0 ≤ x, y≤ 0
19	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(x2 − y2), 2z= x2 + y2, z= 0, если x≤ 0, y≥ 0
20	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(x2 − y2), 2z= x2 + y2, z= 0, если x≤ 0, y≤ 0
21	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(y2 − x2), 2z= x2 + y2, z= 0, если 0 ≤ x, y≥ 0
22	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(y2 − x2), 2z= x2 + y2, z= 0, если x≤ 0, y≥ 0
23	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(y2 − x2), 2z= x2 + y2, z= 0, если x≤ 0, y≤ 0
24	,,, x2 + y2 dxdydz (V)	(x2 + y2)2 = 4(y2 − x2), 2z= x2 + y2, z= 0, если 0 ≤ x, y≤ 0
25	,,, x2 + y2 1 dxdydz 2 (V)	x2 + y2 = 2x, x2 + y2 = 4x, x2 + y2 = 4z, z= 0, если 0 ≤ z
26	,,, √x2 + y2dxdydz (V)	x2 + y2 2 = 4xy, x2 + y2 = 2z, z= 0, если 0 ≤ x,0 ≤ y

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Задание 7. Вычислить интеграл, если область интегрирования

(V ) ограничена поверхностями с заданными уравнениями.

№	Интеграл	Область интегрирования (V)
1	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = x, y= 0, z= 0 при 0 ≤ y, 0 ≤ z
2	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = x, y= 0, z= 0 при 0 ≤ y, z≤ 0
3	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = x, y= 0, z= 0 при y≤ 0, 0 ≤ z
4	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = x, y= 0, z= 0 при y≤ 0, z≤ 0
5	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −x, y= 0, z= 0 при 0 ≤ y, 0 ≤ z
6	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −x, y= 0, z= 0 при 0 ≤ y, z≤ 0
7	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −x, y= 0, z= 0 при y≤ 0, 0 ≤ z
8	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −x, y= 0, z= 0 при y≤ 0, z≤ 0
9	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = y, x= 0, z= 0 при 0 ≤ x, 0 ≤ z
10	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = y, x= 0, z= 0 при 0 ≤ x, z≤ 0
11	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = y, x= 0, z= 0 при x≤ 0, 0 ≤ z
12	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = y, x= 0, z= 0 при x≤ 0, z≤ 0
13	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = y, x= 0, z= 0 при x≤ 0, z≤ 0
14	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −y, x= 0, z= 0 при 0 ≤ x, z≤ 0
15	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −y, x= 0, z= 0 при x≤ 0, z≥ 0
16	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −y, x= 0, z= 0 при x≤ 0, z≤ 0
17	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = z, x= 0, y= 0 при 0 ≤ x, 0 ≤ y
18	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = z, x= 0, y= 0 при 0 ≤ x, y≤ 0

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19	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = z, x= 0, y= 0 при x≤ 0, 0 ≤ y
20	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = z, x= 0, y= 0 при x≤ 0, y≤ 0
21	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −z, x= 0, y= 0 при 0 ≤ x, 0 ≤ y
22	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −z, x= 0, y= 0 при 0 ≤ x, 0 ≤ y
23	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −z, x= 0, y= 0 при x≤ 0, 0 ≤ y
24	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = −z, x= 0, y= 0 при x≤ 0, y≤ 0
25	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = 8x, z= 0 при z≥ 0
26	,,, z3dxdydz (V)	(x2 + y2 + z2)2 = 4x, z= 0 при z≤ 0

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