Задание 7.20

Найдите длину дуги кривой, заданной указанными уравнениями.

1. x = e^-2tcos3t, y = e^-2tsin3t, 0 £ t £ p ¤ 6;

2. x = 4(t – sint), y = 4(1 – cost), 0 £ t £ p ¤ 2;

3. x = 3(cost + tsint), y = 3(sint – tcost), 0 £ t £ p ¤ 3;

4. x = e^2tsin4t, y = e^2tcos4t, 0 £ t £ p ¤ 8;

5. x = (t² – 2) sint + 2tcost, y = (2 – t²) cost+2tsint, 0 £ t £ p;

6. x = 3(1 – sint), y = 3(t – cost), 0 £ t £ p ¤ 2;

7. x = e^4tcos2t, y = e^4tsin2t, 0 £ t £ p ¤ 6;

8. x = 8cos³t, y = 8sin³t, 0 £ t £ p ¤6;

9. x = 3(2cost – cos2t), y = 3(2sint – sin2t), 0 £ t £ p ¤ 2;

10. x = e^3tsin2t, y = e^3tcos2t, 0 £ t £ p ¤ 4;

11. x = e^t(cost + sint), y = e^t(cost – sint), 0 £ t £ p ¤ 2;

12. x = 4(2cos2t – cos4t), y = 4(2sin2t – sin4t), p ¤ 4£ t £ p ¤ 2;

13. x = e^-4tcos3t, y = e^-4tsin3t, 0 £ t £ p ¤ 12;

14. x = 1 – cos3t, y = t – sin3t, 0 £ t £ p ¤ 6;

15. x = 5(3sin2t – 2sin3t), y = 5(3cos2t – 2cos3t), 0 £ t £ p ¤ 2;

16. x = e^-tcos4t, y = e^-tsin4t, 0 £ t £ p ¤ 8;

17. x = (t² – 2)sint + 2tcost, y = (2 – t²)cost + 2tsint, 0 £ t £ p ¤ 2;

18. x = 2(t – sint), y = 2(1 – cost), 0 £ t £ p ¤ 2;

19. x = 6(4cost – cos4t), y = 6(4sint – sin4t), 0 £ t £ p ¤ 6;

20. x = e^-3tsin2t, y = e^-3tcos2t, 0 £ t £ p ¤ 2;

21. x = 3(t – cos3t), y = 3(1 – sin3t), 0 £ t £ p ¤ 2;

22. x = 5(cos4t – 2cos2t), y = 5(sin4t – 2sin2t), 0 £ t £ p ¤ 2;

23. x = e^tsin5t, y = e^tcos5t, 0 £ t £ p ¤ 10;

24. x = e^4tcos2t, y = e^4tsin2t, 0 £ t £ p ¤ 6;

25. x = 8sint + 6cost, y = 6sint – 8cost, 0 £ t £ p ¤ 2;

26. x = 7(3sint – sin3t), y = 7(3cost – cos3t), p£ t £ 3p ¤ 2;

27. x = 4(1 – cos2t), y = 4(t – sin2t), 0 £ t £ p ¤ 2;

28. x = e^-3tcos4t, y = e^-3tsin4t, 0 £ t £ p ¤ 8;

29. , , 0 £ t £ p/4;

30. x = 4(3cos2t – cos6t), y = 4(3sin2t – sin6t), 0 £ t £ p ¤ 2.