חדו״א — כיתה י"ב · 4 יח"ל (קל)

פתרונות

1. 25 — $F(x) = x^{2}. F(5) - F(0) = 25 - 0 = 25$.
2. 27 — $F(x) = x^{3}. F(3) - F(0) = 27 - 0 = 27$.
3. 16 — $F(x) = 2x^{3}. F(2) - F(0) = 16 - 0 = 16$.
4. 36 — $F(x) = 4x^{2}. F(3) - F(0) = 36 - 0 = 36$.
5. 72 — $F(x) = \frac{1}{3}x^{3}. F(6) - F(0) = 72 - 0 = 72$.
6. 40 — $F(x) = \frac{5}{2}x^{2}. F(4) - F(0) = 40 - 0 = 40$.
7. 32 — $F(x) = 4x^{3}. F(2) - F(0) = 32 - 0 = 32$.
8. 20 — $F(x) = 5x^{2}. F(2) - F(0) = 20 - 0 = 20$.
9. 16 — $F(x) = x^{4}. F(2) - F(0) = 16 - 0 = 16$.
10. 18 — $F(x) = \frac{2}{3}x^{3}. F(3) - F(0) = 18 - 0 = 18$.
11. 3 — $F(x) = 3x^{3}. F(1) - F(0) = 3 - 0 = 3$.
12. 36 — $F(x) = x^{2}. F(6) - F(0) = 36 - 0 = 36$.
13. 49 — $F(x) = x^{2}. F(7) - F(0) = 49 - 0 = 49$.
14. 64 — $F(x) = x^{3}. F(4) - F(0) = 64 - 0 = 64$.
15. 50 — $F(x) = 2x^{2}. F(5) - F(0) = 50 - 0 = 50$.
16. 54 — $F(x) = 2x^{3}. F(3) - F(0) = 54 - 0 = 54$.
17. 32 — $F(x) = \frac{1}{2}x^{2}. F(8) - F(0) = 32 - 0 = 32$.
18. 108 — $F(x) = 4x^{3}. F(3) - F(0) = 108 - 0 = 108$.
19. 90 — $F(x) = \frac{5}{2}x^{2}. F(6) - F(0) = 90 - 0 = 90$.
20. $\frac{128}{3}$ — $F(x) = \frac{2}{3}x^{3}. F(4) - F(0) = \frac{128}{3} - 0 = \frac{128}{3}$.
21. 75 — $F(x) = 3x^{2}. F(5) - F(0) = 75 - 0 = 75$.
22. 81 — $F(x) = x^{4}. F(3) - F(0) = 81 - 0 = 81$.
23. 24 — $F(x) = 3x^{3}. F(2) - F(0) = 24 - 0 = 24$.
24. 243 — $F(x) = \frac{1}{3}x^{3}. F(9) - F(0) = 243 - 0 = 243$.
25. 56 — $F(x) = \frac{7}{2}x^{2}. F(4) - F(0) = 56 - 0 = 56$.
26. $\frac{3}{7}x^{7} + c$ — כלל החזקה: $\int 3x^{6}dx = 3 \cdot x^{7}/7 + c = \frac{3}{7}x^{7} + c$.
27. $\frac{4}{3}x^{3} + c$ — כלל החזקה: $\int 4x^{2}dx = 4 \cdot x^{3}/3 + c = \frac{4}{3}x^{3} + c$.
28. $\frac{5}{4}x^{4} + c$ — כלל החזקה: $\int 5x^{3}dx = 5 \cdot x^{4}/4 + c = \frac{5}{4}x^{4} + c$.
29. $x^{6} + c$ — כלל החזקה: $\int 6x^{5}dx = 6 \cdot x^{6}/6 + c = x^{6} + c$.
30. $\frac{7}{4}x^{4} + c$ — כלל החזקה: $\int 7x^{3}dx = 7 \cdot x^{4}/4 + c = \frac{7}{4}x^{4} + c$.
31. $\frac{8}{5}x^{5} + c$ — כלל החזקה: $\int 8x^{4}dx = 8 \cdot x^{5}/5 + c = \frac{8}{5}x^{5} + c$.
32. $\frac{9}{4}x^{4} + c$ — כלל החזקה: $\int 9x^{3}dx = 9 \cdot x^{4}/4 + c = \frac{9}{4}x^{4} + c$.
33. $\frac{10}{3}x^{3} + c$ — כלל החזקה: $\int 10x^{2}dx = 10 \cdot x^{3}/3 + c = \frac{10}{3}x^{3} + c$.
34. $\frac{11}{3}x^{3} + c$ — כלל החזקה: $\int 11x^{2}dx = 11 \cdot x^{3}/3 + c = \frac{11}{3}x^{3} + c$.
35. $\frac{12}{5}x^{5} + c$ — כלל החזקה: $\int 12x^{4}dx = 12 \cdot x^{5}/5 + c = \frac{12}{5}x^{5} + c$.
36. $\frac{13}{2}x^{2} + c$ — כלל החזקה: $\int 13xdx = 13 \cdot x^{2}/2 + c = \frac{13}{2}x^{2} + c$.
37. $4x^{4} + c$ — כלל החזקה: $\int 16x^{3}dx = 16 \cdot x^{4}/4 + c = 4x^{4} + c$.
38. $\frac{2}{9}x^{9} + c$ — כלל החזקה: $\int 2x^{8}dx = 2 \cdot x^{9}/9 + c = \frac{2}{9}x^{9} + c$.
39. $\frac{3}{8}x^{8} + c$ — כלל החזקה: $\int 3x^{7}dx = 3 \cdot x^{8}/8 + c = \frac{3}{8}x^{8} + c$.
40. $\frac{4}{7}x^{7} + c$ — כלל החזקה: $\int 4x^{6}dx = 4 \cdot x^{7}/7 + c = \frac{4}{7}x^{7} + c$.