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Ldaniel

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 ≈

  • one year ago
  • one year ago

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  1. inkyvoyd
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    set 2sin(x^2)=0

    • one year ago
  2. inkyvoyd
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    Wait, over an interval -_-

    • one year ago
  3. inkyvoyd
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    Ignore the interval, and just solve that trig equation.

    • one year ago
  4. Ldaniel
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    i know that the answer for part "a" is

    • one year ago
  5. Ldaniel
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    square(pi)

    • one year ago
  6. inkyvoyd
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    square or sqrt?

    • one year ago
  7. Ldaniel
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    i dont know how to do part b

    • one year ago
  8. Ldaniel
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    sqrt

    • one year ago
  9. inkyvoyd
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    Well, your interval s defined only up to 3. Is that supposed to be that way, or is the three suposed to be pi?

    • one year ago
  10. Ldaniel
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    up to 3

    • one year ago
  11. RaphaelFilgueiras
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    a)\[2*\sin(2*x)=0\rightarrow x=k*pi/2\] In this interval x=pi/2

    • one year ago
  12. inkyvoyd
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    Do you understand a though?

    • one year ago
  13. Ldaniel
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    well i got x= |dw:1334814197335:dw|

    • one year ago
  14. inkyvoyd
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    |dw:1334814169184:dw|

    • one year ago
  15. Ldaniel
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    and is the right answer

    • one year ago
  16. inkyvoyd
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    |dw:1334814236680:dw|

    • one year ago
  17. inkyvoyd
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    Naturally, sqrt pi would be the largest value up to 3, because it squares out to pi.

    • one year ago
  18. Ldaniel
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    the equation is f(x) = 2sin(x^2)

    • one year ago
  19. Ldaniel
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    sorry about that

    • one year ago
  20. RaphaelFilgueiras
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    \[F(x)=-\cos(2*x)+K'\] \[F(1)=-\cos(2*1)+K'=9\]

    • one year ago
  21. inkyvoyd
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    I know - That is sin x

    • one year ago
  22. inkyvoyd
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    but, sin x^2 is similar to the graph in that it has its highest values at sqrtpi

    • one year ago
  23. Ldaniel
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    sqrt(pi) is the right answer for part a is marking it right

    • one year ago
  24. Ldaniel
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    the part that i dont get how to do is part b

    • one year ago
  25. inkyvoyd
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    Yes. Can you tell me what calc course you are enrolled in?

    • one year ago
  26. Ldaniel
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    calculus I

    • one year ago
  27. inkyvoyd
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    Alright, give me a second.

    • one year ago
  28. Ldaniel
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    2sin(x^2) = 0 x^2 = pi x = sqrt(pi)

    • one year ago
  29. Ldaniel
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    thats how i got my answer

    • one year ago
  30. inkyvoyd
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    Have you learned how to approximate integrals?

    • one year ago
  31. Ldaniel
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    kinda

    • one year ago
  32. Ldaniel
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    thats what we are learning

    • one year ago
  33. inkyvoyd
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    What's it called?

    • one year ago
  34. Ldaniel
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    antiderivatives

    • one year ago
  35. inkyvoyd
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    No, what kind of approximations have you learned?

    • one year ago
  36. inkyvoyd
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    I just figured out how I can solve the problem.

    • one year ago
  37. inkyvoyd
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    Here's the graph, btw

    • one year ago
  38. Ldaniel
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    i dont know

    • one year ago
  39. inkyvoyd
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    http://www.wolframalpha.com/input/?i=integrate+2+sin%28x%5E2%29

    • one year ago
  40. Ldaniel
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    the tittle of this chapter is antiderivatives

    • one year ago
  41. inkyvoyd
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    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

    • one year ago
  42. Ldaniel
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    so how do i do part b?

    • one year ago
  43. inkyvoyd
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    I'm thinking ;)

    • one year ago
  44. inkyvoyd
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    Have you learned trapozoidal approximation?

    • one year ago
  45. Ldaniel
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    no

    • one year ago
  46. noginogi
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    I also have a question for part b... help us figure this out plz

    • one year ago
  47. inkyvoyd
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    http://www.wolframalpha.com/input/?i=+2+sin%28x%5E2%29

    • one year ago
  48. inkyvoyd
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    Alright. that is the graph of f(x)=2 sin(x^2) right?

    • one year ago
  49. inkyvoyd
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    Notice how the waves become wider and wider close to 0.

    • one year ago
  50. inkyvoyd
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    after that, they become thinner and thinner.

    • one year ago
  51. inkyvoyd
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    Now, give me a second to explain something.

    • one year ago
  52. inkyvoyd
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    Let me get htis plot into mathematica, and show you what I'm talking about.

    • one year ago
  53. Ldaniel
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    k

    • one year ago
  54. inkyvoyd
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    • one year ago
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  55. inkyvoyd
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    Ok. The area of a>b>c>d Tell me if you understand.

    • one year ago
  56. inkyvoyd
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    @Ldaniel ?

    • one year ago
  57. Ldaniel
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    yes i do

    • one year ago
  58. inkyvoyd
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    So, because of this, we know that from 0 to 3, the area enclosed in a is the greatest

    • one year ago
  59. Ldaniel
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    yes

    • one year ago
  60. inkyvoyd
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    So we are essentially looking for the area there.

    • one year ago
  61. inkyvoyd
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    @FoolForMath , I give up/

    • one year ago
  62. Ldaniel
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    ;/

    • one year ago
  63. inkyvoyd
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    I can give you the answer though, me being a cheater cheater.

    • one year ago
  64. noginogi
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    what's the answer?

    • one year ago
  65. mr.luna
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    i wish i could do this math. -_-

    • one year ago
  66. inkyvoyd
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    Give me a second.

    • one year ago
  67. inkyvoyd
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    I'm going to numerically evaluate the integral with wolfram Mathematica

    • one year ago
  68. inkyvoyd
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    1.78966

    • one year ago
  69. inkyvoyd
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    @lgbasallote , here you go.

    • one year ago
  70. Ldaniel
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    the answer is wrong

    • one year ago
  71. inkyvoyd
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    WHAT?

    • one year ago
  72. inkyvoyd
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    Try the square root of pi then.

    • one year ago
  73. Ldaniel
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    as the answer?

    • one year ago
  74. inkyvoyd
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    Yes.

    • one year ago
  75. Ldaniel
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    wrong

    • one year ago
  76. inkyvoyd
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    btw, try 1.790 if you haven't already.

    • one year ago
  77. Ldaniel
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    i did its wrong

    • one year ago
  78. inkyvoyd
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    Ahem.

    • one year ago
  79. Ldaniel
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    ;(

    • one year ago
  80. lgbasallote
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    lol why call me =)) i only know algebra :P i dont like these stuffs

    • one year ago
  81. Ldaniel
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    :((

    • one year ago
  82. inkyvoyd
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    Wrong, call >.<

    • one year ago
  83. inkyvoyd
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    http://www.wolframalpha.com/input/?i=integral%5B2+sin%28x%5E2%29%2C%7Bx%2C0%2Csqrt%28pi%29%7D%5D

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

    • one year ago
  85. inkyvoyd
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    Got any more info about what you are learning right now?

    • one year ago
  86. inkyvoyd
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    If I used the methods they gave, I might just get the answer they are looking for.

    • one year ago
  87. Ldaniel
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    i got the answer is y = 10.16912...

    • one year ago
  88. inkyvoyd
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    That's th correct answer?

    • one year ago
  89. Ldaniel
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    |dw:1334818371099:dw|

    • one year ago
  90. Ldaniel
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    yes

    • one year ago
  91. dumbcow
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    so\[\int\limits_{1}^{\sqrt{\pi}}f(x) = F(\sqrt{\pi}) - F(1)\] all you need to do is find approximation for definite integral

    • one year ago
  92. inkyvoyd
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    Well, then I'm completely useless.

    • one year ago
  93. Ldaniel
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    10.170 is the answer

    • one year ago
  94. inkyvoyd
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    Nice job.

    • one year ago
  95. Ldaniel
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    thanks anyways

    • one year ago
  96. Ldaniel
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    how old are you?

    • one year ago
  97. inkyvoyd
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    15

    • one year ago
  98. inkyvoyd
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    I'm still not sure how I missed that problem so badly. :/

    • one year ago
  99. Ldaniel
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    15? really?

    • one year ago
  100. dumbcow
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    http://www.wolframalpha.com/input/?i=integrate+2sin%28x^2%29+dx+from+1+to+sqrt%28pi%29 add 9 to get answer

    • one year ago
  101. Ldaniel
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    yes dumbcow

    • one year ago
  102. dumbcow
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    sorry for being redundant, i know you already got the answer just putting it out there for everyones benefit

    • one year ago
  103. apoorvk
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    I believe graph would go like this. (the pitch decreasing with increase in x) |dw:1334819574505:dw|

    • one year ago
  104. inkyvoyd
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    btw, yes, I'm trying to jump the gun and finish calculus and some math afterwards before I enter college.

    • one year ago
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