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# 2016BC2.py

calcpage Jun 23rd, 2016 874 Never
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1. #!/usr/bin/python
2. #MrG 2016.0623 2016BC2
3. #2a) x(3)=14.377, y(3)=-0.5
4. from math import sin, sqrt
5.
6. def f(t):
7.     return t**2+sin(3*t**2)
8.
9. print "x(3) = "
10. a=float(0)
11. b=float(3)
12. for x in range(5):
13.     n=10**x
14.     h=(b-a)/n
15.     l=sum([f(a+i*h)*h for i in range(n)])
16.     r=l-f(a)*h+f(b)*h
17.     print 5+(l+r)/2
18.
19. #2b) dy/dx=0.050 when t=3
20. print
21. print "dy/dx when t is 3 = ", 0.5/f(3)
22.
23. #2c) abs(v(3))=9.969
24. print
25. print "abs(v(3)) = ", sqrt(f(3)**2+0.5**2)
26.
27. #2d) l=4.350
28. def g(t):
29.     return sqrt(f(t)**2+4)
30.
31. print
32. print "l1 = "
33. a=float(0)
34. b=float(1)
35. for x in range(5):
36.     n=10**x
37.     h=(b-a)/n
38.     l=sum([g(a+i*h)*h for i in range(n)])
39.     r=l-g(a)*h+g(b)*h
40.     l1=(l+r)/2
41.     print l1
42.
43. def g(t):
44.     return sqrt(f(t)**2)
45.
46. print
47. print "l2 = "
48. a=float(1)
49. b=float(2)
50. for x in range(5):
51.     n=10**x
52.     h=(b-a)/n
53.     l=sum([g(a+i*h)*h for i in range(n)])
54.     r=l-g(a)*h+g(b)*h
55.     l2=(l+r)/2
56.     print l2
57.
58. print
59. print "l1+l2 = ", l1+l2
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