Кратные, криволинейные и поверхностные интегралы. Логинов А.Ю - 117 стр.

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117
12.7.
2
22
22
59, 4,
44,
42.
xy x
zx xy
zx xy
=- =-
=+--
=+- +
12.8.
2
22
22
61, 5,
2,
24.
y
xy
zxxy
zxxy
=- =
=+-
=+-+
12.9.
22
22
22
51, 31,
26,
16.
xy x y
zxy
zxy
=- =-+
=- +
=- - +
12.10.
2
22
22
37, 4,
26 ,
36 .
xy x
zxy
zxy
=- + =
=+ +
=+ +
12.11.
2
22
22
53, 2,
2361,
2362.
y
xy
zx yy
zx yy
=- + =-
=-- -
=-- +
12.12.
22
22
22
5, 3,
45 8,
15 8.
y
xyx
zxy
zxy
=- =-+
=+ +
=+ +
12.13.
2
22
22
35, 2,
216,
816.
xy x
zxy
zxy
=- =-
=- +
=- +
12.14.
22
22
22
2, 4 3,
16 2,
16 1.
xy x y
zxy
zxy
=- =- +
=--+
=---
12.15.
2
22
22
21, 1,
53,
56.
y
xy
zx y
zx y
=- =
=- -
=- -
12.16.
22
22
22
2, 4 3,
2,
1.
y
xyx
zxy
zxy
=- =- +
=+ +
=- + +
12.17.
2
22
22
41, 3,
71,
72.
xy x
zx y
zx y
=- + =-
=- -
=- +
12.18.
22
22
22
76, 23,
312 5,
212 5.
xy x y
zyx
zyx
=- =-+
=- +
=- - +
12.19.
2
22
22
12, 1,
22,
21.
y
xy
zx yy
zx yy
=- =-
=++-
=+++
12.20.
22
22
22
7, 8 2,
312 5,
212 5.
y
xyx
zyx
zyx
=- =- +
=- +
=- - +
12.21.
2
22
22
23, 5,
19 4,
49 4.
xy x
zxy
zxy
=+ =
=+ +
=+ +
12.22.
2
22
22
34, 7,
52 3,
12 3.
y
xy
zxy
zxy
=+ =
=- +
=- +
     x = 5y 2 - 9, x = - 4,                y = 6x 2 - 1, y = 5,
12.7. z = x 2 + 4x - y 2 - 4,        12.8. z = 2x 2 + x - y 2 ,
     z = x 2 + 4x - y 2 + 2.               z = 2x 2 + x - y 2 + 4.

     x = 5y 2 - 1, x = - 3y 2 + 1,          x = - 3y 2 + 7, x = 4,

12.9. z = 2 -    x 2 + 6y 2 ,        12.10. z = 2 +    6x 2 + y 2 ,

     z = - 1-      x 2 + 6y 2 .             z = 3+     6x 2 + y 2 .

       y = - 5x 2 + 3, y = - 2,             y = x 2 - 5, y = - x 2 + 3,

12.11. z = 2x 2 - 3y - 6y 2 - 1,     12.12. z = 4 +     5x 2 + 8y 2 ,
       z = 2x 2 - 3y - 6y 2 + 2.            z = 1+     5x 2 + 8y 2 .

       x = 3y 2 - 5, x = - 2,               x = y 2 - 2, x = - 4y 2 + 3,

12.13. z = 2 -    x 2 + 16y 2 ,      12.14. z =    16 - x 2 - y 2 + 2,

       z = 8-     x 2 + 16y 2 .             z =    16 - x 2 - y 2 - 1.

       y = 2x 2 - 1, y = 1,                 y = x 2 - 2, y = - 4x 2 + 3,

12.15. z = x 2 - 5y 2 - 3,           12.16. z = 2 +    x 2 + y2,
       z = x 2 - 5y 2 - 6.                  z = - 1+     x2 + y2.

       x = - 4y 2 + 1, x = - 3,             x = 7y 2 - 6, x = - 2y 2 + 3,
12.17. z = x 2 - 7y 2 - 1,           12.18. z = 3 - 12y 2 + 5x 2 ,
       z = x 2 - 7y 2 + 2.                  z = - 2 - 12y 2 + 5x 2 .

       y = 1 - 2x 2 , y = - 1,              y = x 2 - 7, y = - 8x 2 + 2,
12.19. z = x 2 + 2y + y 2 - 2,       12.20. z = 3 - 12y 2 + 5x 2 ,
       z = x 2 + 2y + y 2 + 1.              z = - 2 - 12y 2 + 5x 2 .

       x = 2y 2 + 3, x = 5,                 y = 3x 2 + 4, y = 7,

12.21. z = 1 +    9x 2 + 4y 2 ,      12.22. z = 5 -    2x 2 + 3y 2 ,

       z = 4+     9x 2 + 4y 2 .             z = 1-     2x 2 + 3y 2 .

                                     117

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