Wydział: WiLiŚ, Budownictwo i Transport, sem.1

dr Jolanta Dymkowska Całka oznaczona Oblicz:

π

2

2

π

1. R x4+1 dx 2. R ctg x dx 3.

R

cos2 x dx

x2

1

π

−π

4

π

π

4

2

10

4. R sin4 x dx 5.

R

sin2 x cos2 x dx 6.

R

x2008 sin x e−x2 dx 0

− π

−10

2

1

7

1

7.

R

x8 arcsin x dx 8.

R

x4 ln 9−x dx 9.

R

|x|x2 dx

9+x

−1

−7

−1

e

π

4

√

10. R x | ln x| dx 11. R | cos x| dx 12. R x 3 x2 + 9 dx 1

0

0

eπ

π

2

3

2

13. R (x + 1) cos x dx 14. R

x

dx

15. R

e2x

dx

sin2 x

1+ex

0

π

0

4

√

1

2

2

e

2

16. R x arctg 2x dx 17. R x2 ln2 x dx 18.

R

x2 arcsin x

√

dx

1−x2

0

1

0

5

6

ln 8

19. R

x

√

dx

20.

R

3−x

√

dx

21.

R

1

√

dx

4x+5

3 x+2

ex+1

1

−1

ln 3

1

3

3

2

22. R

1

dx

23. R

1

dx

24. R x3+x2−x+1 dx 4x2−9

x+x3

x2−1

2

1

0

π

π

π

4

3

3

25. R tg 3x dx 26.

R

sin3 x cos4 x dx 27. R

1

dx

sin3 x cos x 0

− π

π

2

4

√

4

1

2

q

√

28. R

1

√

dx

29. R

2+x dx

30.

R

2 − x2 dx

(1+

x)2

2−x

1

0

1

π

3

0

2

31. R

sin 2x

√

dx

32.

R

ln(1 − x) dx 33.

R

3x−7

dx

x3+x2+4x+4

0

1+sin2 x

−2

−2

π

2

1

0

34. R

1

dx

35. R

1

dx

36.

R

x−4

dx

3+cos x

1+ex

x2−5x+4

0

0

−1

π

2

2

1

37. R

1

dx

38. R

1

dx

39. R

1√ dx

1+sin x+cos x x(x2+1)

1+

x

0

1

0

1

40.

R

x

ex dx

(1+x)2

−1