Matematyka, RMT, MTA

2010/2011, sem. letni

Całki oznaczone

Zad.1. Obliczyć całki:

(1)

R

1

−2

(x

2

− x + 2)dx,

(2)

R

π

3

π

6

1

sin

2

x

dx,

(3)

R

π

2

−

π

4

(2 sin x − 5 cos x)dx,

(4)

R

1

√

3

3

dx

x

2

+1

,

(5)

R

log

3

5

0

3

x

dx,

(6)

R

2

1

2x+9

x−3

dx,

(7)

R

1

0

dx

x

2

+6x+9

,

(8)

R

2

0

x

3

x

4

+1

dx,

(9)

R

2

1

x+1

x

2

+6x+5

dx,

(10)

R

3

2

dx

x

3

+x

2

,

(11)

R

2

1

x+2

x

5

+x

3

dx,

(12)

R

π

3

−

π

6

cos

4

xdx,

(13)

R

0

−1

(2x + 1)e

3x

dx,

(14)

R

e

2

1

x

2

ln xdx,

(15)

R

1

−1

x

2

arctgxdx,

(16)

R

0

−

π

2

x

2

cos xdx,

(17)

R

0

−1

x

2

ln(x

2

+ 1)dx,

(18)

R

1
2

0

e

100x

dx,

(19)

R

0

−2

3

√

4x − 1dx,

(20)

R

0

−1

6x

2

√

x

3

+ 1dx,

(21)

R

π

2

0

cos

5

x sin xdx,

(22)

R

7π

6

5π

6

sin

5

xdx,

(23)

R

2

1

x

q

2x−1

x+3

dx,

(24)

R

e

2

e

ln

4

x

x

dx,

(25)

R

e−2

−1

ln(x + 2)dx,

(26)

R

√

3

0

arctg

3

x

x

2

+1

dx,

(27)

R

1

−1

dx

e

x

+1

,

(28)

R

1

0

e

x

e

2x

−1

dx,

(29)

R

4

1

√

x−1

√

x+1

dx,

(30)

R

9

1

x

√

x+1

x+

√

x

dx,

(31)

R

π

4

π

6

dx

sin x

,

(32)

R

−1

−2

1

x

2

e

1
x

dx,

(33)

R

π

3

π

4

tg

3

x

cos

2

x

dx,

(34)

R

π

3

π

6

cos

2

x−2

sin

2

x+2

dx.

1