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