Контрольная Интегралы и дифференциальные уравнения №2

À

Â

Ñ

D

R ln(x2

R

(14 + 25x + 3x2)dx

R

xdx

R

2

+ 4)dx

(x2

+ 2x 1)dx

dx

(2x 6)dx

1

esin x sin 2xdx

(1 + x)(5 + x)(1 + 2x)

px2

6x + 1

(tg2 2x + tg3 2x)dx

p

x3 x

cos3 x sin x

2x x2

3

Rx tg x sec xdx

R

(10x + x2 3)dx

R

(2x 5)dx

Rctg3(x=4)dx

4

Rex2 (x + x3)dx

R

(x2

7x 2)dx

R

(x 1)dx

R

dx

(x2

x)(x + 3)

x2

4x + 8

R ex(x2

R(x2 8x 16)dx

R

cosR

5

2)dx

3

2x sin 2xdx

p

(x 1)dx

(x3 x2 2x)

x2

4x + 5

cos x + 1

6

Rln(px + 1)dx

R

R

R

tg5(2x)dx

(2x2

3x + 9)dx

2xdx

(x3 16x)

2x2

+ 4x + 3

p

Re2x arctg exdx

R

R

Rctg5(3x)dx

(x3 9x)

9x x2

7

(5x 9)dx

(2x 1)dx

(x3 6x2 + 9x)

x2 + 2x + 2

R

R

R

sinR

8

arcsin x

dx

(x 4)dx

(x 0; 5)dx

4 2x cos 2xdx

(x2 + 2x 12)dx

(2x + 1)dx

9

ecosRx(cos x sin2 x)dx

R

R

R

dx

x3

(x3

4x2 + 4x)

x2 + 3x

10

R

arctg xdx

R

R

R

(10 + 2x 3x2)dx

(x + 3)dx

sin x

dx

(x 1)(x 2)(x + 2)

x2 + 8x + 15

cos2 x sin4 x

11

Rln(x2

+ x3)dx

R

R

R

(5x2

8x 19)dx

(x + 8)dx

dx

x2

(x 4)(1 + x)(2 + x)

x2

2x + 5

sin x + 2

eRx(sin x + cos x)dx

R

R(4x 2)dx

R

12

(x2

7x + 1)dx

tg xdx

(1 + x)(3 + x)(x 2)

px2

8x

1 sin x

R

arctg(px)dx

R(4x2

3x 2)dx

R

R

13

dx

(x2 3)dx

(1 + x)2(x 2)

p

x2

2x + 10

cos3 x sin x

14

R

R

R

R

arctg xdx

(5x + 3x2 8)dx

p

8xdx

2

2

dx

(1 + x)2(x 4)

x2 + 6x

cos5 x sin x

R

R

R

R

(4 + 3x + 3x2)dx

4

(2x

3)dx

(1 + x)(2 + x)(x 4)

4x

2x

1

cos x

15

R x(2 ln x + 1)dx

R

R

p

Rcos 3xdx

(1 + x)(2 + x)(x 3)

x2 3x + p

8

âàð.

Кривые

1

x2 + y2 = 2; y = x2

2

(x 2)(y + 3) = 6; x + y = 6

3

y = x2 4; x + y = 2

4

x2 + y2 = 3; y2 = 2x

5

y = x2 4x + 3, касательная к ней в точке x = 4, ось OY

6

y2 = 4x; x2 = 4y

7

y = cos x(îäíà àðêà);

x + y = 1

2

8

y = 1 ; x + y =

5

x

2

9

y = x2 4x + 2; x + y = 2

10

x2 + y2 = 1; x + y = 1

11

y = x2; y = (x 2)2,

îñü OX

12

x2 + y2 = 3; x2 = 2y

13

x2 + y2 = 5; x2 = 4y

14

x2 + y2 = 1; y = jxj

15

(x 1)2 + y2 = 1; y = x2

âàð.

Поверхности

1

x2 + z2 = 5y2 4; x2 + z2 = (y 2)2

2

y2 + z2 = x; y2 + z2 = x2

3

x2 + z2 = y; y = 1

4

x2 + y2 = 2z; x2 + y2 + z2 = 8

5

x2 + y2 = z2 + 1; z = 1; z = 2

6

y2 + z2 = x2 + 1; y2 + z2 = 2x2

7

y2 + z2 = x2; x2 + y2 + z2 = 8

8

x2 + z2 = y2 + 1; x2 + z2 = 2

9

y2 + z2 = 3x2; x2 + y2 + z2 = 4

10

x2 + z2 = y2 1; y = 2

11

x2 + y2 = z2 1; x2 + y2 = 2(z 1)2

12

x2 + z2 = y2 + 1; x2 + z2 = 5

13

x2 + y2 + z2 = 4; x2 + (y 2)2 + z2 = 4

14

4x2 + y2 + 4z2 = 4; y = 1

15

x2 + y2 + z2 = 5; x2 + y2 = 1

À

Â

A

B

+1 sin2 x

1

x2dx

+1 ln xdx

=4 sin x

1

R1

dx

R0

9

R1

p

R0

xp

dx

x2

3

(1 x2)5

x3 + 1

x

+1

dx

p1 dx

+1

x13

1

dx

2

R4

x2 + p3

R0

10

R1

dx

R0

ep

1

(x5 + x3 + 1)5

x4 + 1

x

3

x(ex e x)

+1 x arctg x

1

p

+1 (2x + 1) sin(1=2x)

1psin(1=x)

xdx

3

R0

p3

dx

R0

11

R1

p5

dx

1R=2

p

dx

esin x 1

1 + x4

x6 + 5x 2

1 x

4

+1

cos 2x

dx

1

dx

12

+1 2 3 sin xdx

3

xdx

R

R

R

R

1

p

x5 + 3x4 + 1

0

ex cos x

3

x3 + x

0

p3

1 + x2

1

+

1

sin 3x

=2

ln(1 + sin x)

+

1 arctg x

1

dx

R

R

+R

2R

5

1

p3 x5 + 2x + 4dx

0

px3

dx

13

1

x

dx

0

p4 1 x4

+

1

x + sin x

dx

1 2 + cos x

2

x

sin

R

R

R +

2R

+

3=x

4

6

1

x3(x sin x)dx

0

sin8 x

14

1

px

dx

0

(2

x)2 dx

1 e

1

dx

1

sin x

ln(p

+ 1)

dx

7

dx

15

dx

x

R2

px2 + 4

R0

sin5 x

R1

x2

R0

etg x 1

=2

+

1

xdx

cos x

1

8

R2

p

R0

dx

x4 + 1

x3

âàð.

À

Â

1

dx

+

dy

= 0

dy

+

2y

= x3

x(y

dx

1)

y(x + 2)

x

ye y2 sin ydy = dx + 2xydy

2

4 + y2dx ydy = x2ydy

3

p

dx

=

dy

xydx = (3x2 + 4y)dy

y x

y + x

4

xy0 y = y3

(y2 + 2y + x2)y0 + 2x = 0

5

y0 tg x = y

y0 cos x + y sin x = 1

6

(3x2 y2)dx = 2xydy

y0 y = 2xex

8

0

=

+ p

0 +

2

3

7

xy

y

y2

x2

y

y = 6x + 3x2

xy0 = x + y

(xy + x y )dy = dx

9

y0 =

y

2

y2dx (2xy + 3)dy = 0

x

10

(xy

x)dx + (xy + x

y