Domashka_po_matematike

ВАРИАНТ 8

5

π

10

x × dx

dx

ò4 tg3x ×sec2x × dx .

1.

ò

;

ò

;

2

−

5

20 - x

1 1

+ 3x +1

0

8

9x7 + x3 - 7x

3

2.

ò

12x4 + 5

dx ; ò

x ×arctgx dx .

−8

−

3

f (x)

cos3 x

éπ

π

ù

3.

=

,

ê

;

2

ú.

sin x

ë 3

û

1

4.

ò

x4 - 0,5x2 + 4

dx .

−2

e

e

ln2 x

5.

òe−2x × ln x dx ,

ò

e2x

dx .

1

1

6.

y = 1 − x2 , y = 3

−1, x − 2 = 0.

x

2

dx

∞

dx

7.

ò

;

ò1

.

x2 - 4x + 5

x ×(ln x + 8)

−∞

e−

8.

S = 140, N = 4,

r = 8.

8

8

(x + 2)

π

6

x × dx

12

1.

ò

;

ò

dx ;

òsin3 2x ×cos2xdx .

128 + x2

x +1

−8

2

3

0

9

9x5 - x9

0,5

2.

ò

5x10 +1

dx ;

ò x ×arcsin x

dx .

−9

−0,5

3.

f (x) =

1

,

[2; 4].

e2x - ex

5

x

2

4.

ò

dx .

4

+ 7

−2

x

0

0

5.

ò 3

×sin2 x

dx ,

ò x ×sin2 x × dx .

x

−1

−1

∞

dx

0

dx

òe

−∞ò

7.

;

.

x × 3

(x - 2)4

ln x

8.

S = 160,

N = 4, r = 10.

ВАРИАНТ 10

0,5

4

5

x × dx

dx

arctg2x

1.

ò

;

ò

dx ;

ò2 x ×

.

40 - x2

1+ 4x2

x

− 10

0

1

π

3

2.

ò sin 6x ×

x6 +10

dx ;

ò x4 ×

9 - x2

dx .

−π

−3

3.

f (x) =

ex

, [0; 2].

e2x +

4

π

4.

ò2 ecos2 xdx .

π

4

1

1

5.

ò 1+ (x -1)3 dx ,

ò

x3

dx .

0

0

6.

y = (x - 2)3 , y = 4x - 8.

∞

dx

0

x

7.

ò

;

ò

dx .

3

4

10 + x

2

e3 x ×

ln

x

−∞

8.

S = 125,

N = 4,

r = 10.

0

x × dx

4

−0,25

dx

1+ 2x

1.

−ò9

;

ò

dx ;

−0,25ò

.

2x -1

(1+16x2 )×arctg2 4x

162 - x2

2

3

11

1,5

x4

2.

ò sin 4x ×

x8 + 3

dx ;

ò

dx .

9 - x

2

−11

−1,5

f (x) =

cos3

2x

é

π

π ù

3.

sin 4x

,

ê

-

6

;

ú.

ë

4 û

0

ò

4.

4 + x4 - x2

dx .

−9

4

dx

4

5.

ò

, òe−x2 dx .

e2x

3

3

y =

, y = 0, x = 0, x =1.

6.

4 - x 2

∞

dx

0,5

dx

7.

ò

;

ò

.

(x

-1)

2

(ln x + 2)

5

e2 x ×

−∞

8.

m = 6000,

T = 3,

V = 40000.

7,5

2

x × dx

8

(x +1)

3

0,5π

1.

ò

;

ò

dx ;

ò ctg2x × dx .

x

450 - x

2

−15

3

π

6

2π

2

dx

2.

ò cos2x × 3 7x3 + x

dx ; ò

.

5

−2π

−2

(4 + x2 )

6.

y =

+ 1, y = 3 − x, y = 0, x = 0.

x

34

dx

∞

dx

ò

; ò

7.

.

x2 - 6x +10

3

4x +1

−∞

0

8.

m = 5000,

T = 4,

V = 30000.

BАРИАНТ 13

12

4

π

6

x × dx

dx

3

ò

ò

ò tg2x × dx .

1.

;

;

288 + x2

×(x +1)

x

2

−12

1

−0,25π

13

(x - 5

)

5

x

2.

ò

x8 +13

dx ;

ò x4 25 - x2 dx .

−13

−5

f (x) = ln(

- x) , [0; 2].

3.

1+ x2

1

4.

ò x × 3

5 + x3

dx .

−2

3

3

5.

òex3 dx ,

òe16x dx .

1

1

6.

y = e2x , y = x +1, x −1= 0, x = 0.

∞

3x2 +1

0

dx

7.

ò

x + x

3

dx ;

ò

.

3 (4 - x)

7

1

−∞

8.

m = 7000,

T = 5,

V = 30000.