математика_2семестр

1:

dx f(x; y) dy:

2:

ZZ

18x2y2 + 32x3y3

dxdy; D : x = 1; y = x3

; y = p3

x:

D

3: x = y2 2y; y = x:

p

y = 5p

5x

; z = 0; z = 5 +

5

x

:

4:

x; y =

3

3

1:

dy f(x; y) dx:

1:

dx

f(x; y) dy:

2:

ZZ

8xy + 9x2y2

dxdy; D : x = 1; y = x2

; y = p3

x:

D

3: 3y2 = 25x; 5x2 = 9y:

4:

x + y = 2; y = p

x; z = 0; z = 12y:

1:

dx f(x; y) dy:

2:

ZZ

18x2y2 + 32x3y3

dxdy; D : x = 1; y = x2

; y = p3

x:

D

3: y = x2; 4y = x2; y = 4:

1

4:

x = 20p2y; x = 5p2y; z = 0; z + y =

:

2

1:

dy

f(x; y) dx:

4

p

9+y2

ZZ

2:

27x2y2

+ 48x3y3

dxdy;

D : x = 1; y = x3; y = p

x:

D

3: xy = 4; y = x; x = 4:

5p

; x =

5y

; z = 0; z =

5

(3 + p

) :

4: y =

y

y

2

6

6

1:

dx

f(x; y) dy:

1

2x2

2:

ZZ

4xy + 3x2y2

dxdy; D : x = 1; y = x2

; y = p

x:

D

1:

dx

f(x; y) dy:

2:

ZZ

8xy + 18x2y2

dxdy; D : x = 1; y = x2; y = p3

x:

D

1:

dy f(x; y) dx:

2:

ZZ

5xy + 9x2y2

dxdy;

D : x = 1; y = x3; y = px:

D

4

3: x + 4 = y2; x + 3y = 0:

p

p

1

4: y = 17 2x; y = 2 2x; z = 0; x + z =

:

2

1:

dy

f(x; y) dx:

2:

ZZ

6xy + 24x3y3

dxdy; D : x =

1; y = x2; y = p

x:

D

3: y = x2; y = 6 x; y = 0:

5p

; y =

5x

; z = 0; z =

5 (3 + p

)

4:

y =

x

x

:

3

9

9

1:

dx f(x; y) dy:

3

2x2

2

2:

ZZ 4xy + 16x3y3 dxdy; D : x = 1; y = x3; y = p3

x:

1:

dy

f(x; y) dx:

1:

dx f(x; y) dy:

2:

ZZ

xy 4x3y3

dxdy; D : x = 1; y = x3; y = p

x:

D

3: y = x3; y = 4x:

:

4:

x = 6

; x = 18

; z = 0; z =

18

5p

y

5y

5

3 + p

y

1:

dx f(x; y) dy:

2:

ZZ 3x2y2 + 3 x4y4

dxdy; D : x = 1; y = x3; y = p3

x:

50

D

3: y2 = 9x; y = x + 2:

x = 19p

4:

2y; x = 4p2y; z = 0; y + z = 2:

1:

dx f(x; y) dy:

2:

ZZ

44xy + 16x3y3

dxdy; D : x = 1; y = x2

; y = p3

x:

D

3: y2 = x + 1; y2 = 9 x:

30y

4:

x2 + y2 = 8; x = p2y; x = 0; z = 0; z =

:

11

1:

dx

f(x; y) dy:

2:

ZZ y cos xy dxdy; D : x = 1; x = 2; y = 2

; y = :

D

3: xy = 4; x + y 5 = 0:

x + y = 4; x = p

3x

:

4:

2y; z = 0; z =

5

1:

dx f(x; y) dy:

1:

dx f(x; y) dy:

ZZ

xy

2:

y2e 4 dxdy;

D : x = 0; y = 2; y = x:

D

3: y = 2x x2; y = x:

5p

; y =

5x

5 (3 + p

)

4: y =

x

; z = 0; z =

x

:

6

18

18

1:

dx

f(x; y) dy:

2: ZZ

4ye2xydxdy; D : x = 1; x = 2

; y = ln 3; y = ln 4:

1

D

3: y = p

x; xy = 1; x = 2; y = 0:

4: x2 + y2 = 18; y = p

5x

3x; y = 0; z = 0; z =

:

11

1:

dx

f(x; y) dy:

2:

ZZ

4y2 sin xy dxdy; D : x = 0; y = x; y = r

2 :

D

3: y = x2 + 4; 2x + y 4 = 0:

x + y = 6; y = p

4:

3x; z = 0; z = 4y:

1:

dy f(x; y) dx:

2:

ZZ y sin xy dxdy; D : x = 1; x = 2; y = 2

; y = :

1:

dx f(x; y) dy:

xy

ZZ y2e 2 dxdy; D : x = 0; y = x; y = p

:

2:

2

D

3: y = x2 + 8; y = x2:

4:

z = x2 + y2; y = x2; z = 0; y = 1:

1:

dx f(x; y) dy:

2:

ZZ

2y cos 2xy dxdy; D : x = 1; x = 2; y = 4

; y = y =

2 :

D

p

p

3:

y = 2 x + 1; y = 4 2x; y = 0:

1:

dx f(x; y) dy:

2:

ZZ

8ye4xydxdy; D : x = 4

; x =

2; y = ln 3; y = ln 4:

1

1

D

3: y = (x + 1)2; y2 = x + 1:

4:

y + z = 1; x = y2 + 1; x = 0; y = 0; z = 0:

1:

dx f(x; y) dy:

2:

ZZ

3y2 sin 2 dxdy;

D : x = 0; y =

23

; y = r

43 :

xy

x

Z

p

2z p

1:

L

2 + z2

x2 + y2

dl;

L : x = t cos t; y = t sin t; z = t;

0 6 t 6 2 :

~

2

2

4; 0); B(0; 2):

2:

L

AB; A(

F = x 2y

~{ +

y

2x ~|;

отрезок прямой

3:

ZZ (2x + 3y + 2z)dS; : x + 3y + z = 3:

S

4:

ZZ

3xdydz + (y + z)dxdz + (x z)dxdy;

: x + 3y + z = 3:

S

Вариант 2.

1:

Z

x2 + y2

dl;

L : x2 + y2 = 4:

L

~

2

2

4; 0); B(0; 2):

2:

L

AB; A(

F =

x

+ 2y ~{ + y

+ 2x

~|;

отрезок прямой

3:

ZZ (2 + y 7x + 9z)dS; : 2x y 2z = 2:

S

4:

ZZ (3x 1)dydz + (y x + z)dxdz + 4zdxdy;

: 2x y 2z = 2:

S

Вариант 3.

1:

Z

8

x2

y2

; L отрезок прямой AB; A(0; 0); B(2; 2):

dl

L

p

2:

F~

= x2

+ 2y ~{ + y2

+ 2x

~|;

L : 2

x2

= y; A( 4; 0); B(0; 2):

2

3:

ZZ (6x + y + 4z)dS;

: 3x + 3y + z = 3:

S

4:

ZZ xdydz + (x + z)dxdz + (y + z)dxdy;

: 3x + 3y + z = 3:

S

Вариант 4.

Z

4p3

3p

1:

x

dl;

y

L

L отрезок прямой AB; A( 1; 0); B(0; 1):

2:

~

L : x

2

+ y

2

= 4 (y >

0) ; A(2; 0); B( 2; 0):

F = (x + y)~{ + 2x~{;