Domashka_po_matematike

5

π

6

x

× dx

5

x

ò6

sin 2x

1.

ò

;

ò

dx ;

dx .

2

4

−5

50 + x

−1

4 + x

0 18 - 5cos2x

2

18

(

3

x6

2.

ò

7

×

x4

+10 dx ;

ò

dx .

sin x

9 + x2

)

−18

−3

f (x) =

1

3.

,

é4 2; 8ù.

x ×

x

2

-16

ë

û

−2

0

0

5.

ò 3

3x - x2

dx ,

ò 3

3 - x3

dx .

−5

−5

ì

2

, 0 £ x £1; x = 2

ïx

6.

y = í

1

.

ï

, 1< x £

2; y = 0

2

î x

∞

dx

1

(x - 2)

7.

ò0

;

−∞ò

dx .

(5x + 2)4

x2 - 4x +18

8.

m = 4500,

T = 3, V = 36000.

BАРИАНТ 19

2

4,6

3

10

x × dx

dx

e

ln x

1.

ò

;

ò

;

ò

dx .

3

x

2

5x

−2

5

80 - x

0,24

+ 4 +

1

1

e

19

tg4x

2

x4

2.

ò

dx ;

ò

dx .

9 + x6 + 5x10

x2 + 2

−19

−

2

3.

f (x) = cos x ×cos

2

3x,

é

π ù

ê0;

ú.

ë

2 û

3

4.

ò 4

8 - x2 + x4

dx .

−1

1

1

5.

òearcsin x × x3

dx ;

ò25x × earcsin x

dx .

0

0

ì

1

,

-2 £ x £ -1; y = 0

6.

ï

.

y = í x2

ï

2

,

-1

£ x £ 0; x = -2

îx

−2

dx

∞ arctgx

7.

−∞ò

; ò1 x2 +1

dx .

(3x +1)5

8.

m = 6000,

T = 4,

V = 45000.

10

1

π

3

6

x × dx

6 x

1.

ò

;

ò

dx ;

ò 3 sin2 x ×cosx × dx .

2

3

+ 300

(4

-

x )

−30 x

0

−0,5π

20

20x7 - x

1

2.

ò

dx ;

ò x3 ×arctgx

dx .

x12 + 3x2 + 5

−20

−1

6.

y = e−2x ,

y = e3x ,

x = ln 0,4, x = ln 3.

0

dx

∞

2

7.

ò

; ò

x

dx .

5 (x -1)

6

3

+ 4

−∞

1

5x

8.

m = 7000,

T = 5,

V = 49000.