Ldaniel 3 years ago Consider the function f(x) = 2sin(x2) on the interval 0 ≤ x ≤ 3. (a) Find the exact value in the given interval where an antiderivative, F, reaches its maximum. x = (b) If F(1) = 9, estimate the maximum value attained by F. (Round your answer to three decimal places.) y ≈

1. inkyvoyd

set 2sin(x^2)=0

2. inkyvoyd

Wait, over an interval -_-

3. inkyvoyd

Ignore the interval, and just solve that trig equation.

4. Ldaniel

i know that the answer for part "a" is

5. Ldaniel

square(pi)

6. inkyvoyd

square or sqrt?

7. Ldaniel

i dont know how to do part b

8. Ldaniel

sqrt

9. inkyvoyd

Well, your interval s defined only up to 3. Is that supposed to be that way, or is the three suposed to be pi?

10. Ldaniel

up to 3

11. RaphaelFilgueiras

a)$2*\sin(2*x)=0\rightarrow x=k*pi/2$ In this interval x=pi/2

12. inkyvoyd

Do you understand a though?

13. Ldaniel

well i got x= |dw:1334814197335:dw|

14. inkyvoyd

|dw:1334814169184:dw|

15. Ldaniel

16. inkyvoyd

|dw:1334814236680:dw|

17. inkyvoyd

Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.

18. Ldaniel

the equation is f(x) = 2sin(x^2)

19. Ldaniel

20. RaphaelFilgueiras

$F(x)=-\cos(2*x)+K'$ $F(1)=-\cos(2*1)+K'=9$

21. inkyvoyd

I know - That is sin x

22. inkyvoyd

but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi

23. Ldaniel

sqrt(pi) is the right answer for part a is marking it right

24. Ldaniel

the part that i dont get how to do is part b

25. inkyvoyd

Yes. Can you tell me what calc course you are enrolled in?

26. Ldaniel

calculus I

27. inkyvoyd

Alright, give me a second.

28. Ldaniel

2sin(x^2) = 0 x^2 = pi x = sqrt(pi)

29. Ldaniel

thats how i got my answer

30. inkyvoyd

Have you learned how to approximate integrals?

31. Ldaniel

kinda

32. Ldaniel

thats what we are learning

33. inkyvoyd

What's it called?

34. Ldaniel

antiderivatives

35. inkyvoyd

No, what kind of approximations have you learned?

36. inkyvoyd

I just figured out how I can solve the problem.

37. inkyvoyd

Here's the graph, btw

38. Ldaniel

i dont know

39. inkyvoyd
40. Ldaniel

the tittle of this chapter is antiderivatives

41. inkyvoyd

Note how the function uses something called the fresnal S, which I don't know either. But mor eimportantly, notice how it gets to its peak at about 1,7

42. Ldaniel

so how do i do part b?

43. inkyvoyd

I'm thinking ;)

44. inkyvoyd

Have you learned trapozoidal approximation?

45. Ldaniel

no

46. noginogi

I also have a question for part b... help us figure this out plz

47. inkyvoyd
48. inkyvoyd

Alright. that is the graph of f(x)=2 sin(x^2) right?

49. inkyvoyd

Notice how the waves become wider and wider close to 0.

50. inkyvoyd

after that, they become thinner and thinner.

51. inkyvoyd

Now, give me a second to explain something.

52. inkyvoyd

Let me get htis plot into mathematica, and show you what I'm talking about.

53. Ldaniel

k

54. inkyvoyd

55. inkyvoyd

Ok. The area of a>b>c>d Tell me if you understand.

56. inkyvoyd

@Ldaniel ?

57. Ldaniel

yes i do

58. inkyvoyd

So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest

59. Ldaniel

yes

60. inkyvoyd

So we are essentially looking for the area there.

61. inkyvoyd

@FoolForMath , I give up/

62. Ldaniel

;/

63. inkyvoyd

I can give you the answer though, me being a cheater cheater.

64. noginogi

65. mr.luna

i wish i could do this math. -_-

66. inkyvoyd

Give me a second.

67. inkyvoyd

I'm going to numerically evaluate the integral with wolfram Mathematica

68. inkyvoyd

1.78966

69. inkyvoyd

@lgbasallote , here you go.

70. Ldaniel

71. inkyvoyd

WHAT?

72. inkyvoyd

Try the square root of pi then.

73. Ldaniel

74. inkyvoyd

Yes.

75. Ldaniel

wrong

76. inkyvoyd

btw, try 1.790 if you haven't already.

77. Ldaniel

i did its wrong

78. inkyvoyd

Ahem.

79. Ldaniel

;(

80. lgbasallote

lol why call me =)) i only know algebra :P i dont like these stuffs

81. Ldaniel

:((

82. inkyvoyd

Wrong, call >.<

83. inkyvoyd
84. inkyvoyd

So, you are supposed to use an estimation method that isn't accurate, nor do I know. Or, the problem is set up funy.

85. inkyvoyd

86. inkyvoyd

If I used the methods they gave, I might just get the answer they are looking for.

87. Ldaniel

i got the answer is y = 10.16912...

88. inkyvoyd

89. Ldaniel

|dw:1334818371099:dw|

90. Ldaniel

yes

91. dumbcow

so$\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi}) - F(1)$ all you need to do is find approximation for definite integral

92. inkyvoyd

Well, then I'm completely useless.

93. Ldaniel

94. inkyvoyd

Nice job.

95. Ldaniel

thanks anyways

96. Ldaniel

how old are you?

97. inkyvoyd

15

98. inkyvoyd

I'm still not sure how I missed that problem so badly. :/

99. Ldaniel

15? really?

100. dumbcow
101. Ldaniel

yes dumbcow

102. dumbcow

sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit

103. apoorvk

I believe graph would go like this. (the pitch decreasing with increase in x) |dw:1334819574505:dw|

104. inkyvoyd

btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.