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rld613 Group Title

James?

  • 2 years ago
  • 2 years ago

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  1. neverforgetvivistee Group Title
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    give me edals

    • 2 years ago
  2. JamesJ Group Title
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    so the answer is?

    • 2 years ago
  3. rld613 Group Title
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    oh that was annoying i cldnt type

    • 2 years ago
  4. neverforgetvivistee Group Title
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    give me medals free medals for everyone

    • 2 years ago
  5. rld613 Group Title
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    can you write the equation again please :D

    • 2 years ago
  6. JamesJ Group Title
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    \[ \frac{d \ }{dx} \int_{17}^x \sin(t^2)/t \ dt \]

    • 2 years ago
  7. rld613 Group Title
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    d/dx(sinx^2/x) - d/dx(sin(17)/17)

    • 2 years ago
  8. JamesJ Group Title
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    No

    • 2 years ago
  9. rld613 Group Title
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    where did i go wrong?

    • 2 years ago
  10. JamesJ Group Title
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    look at the earlier example with ln

    • 2 years ago
  11. rld613 Group Title
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    k i will

    • 2 years ago
  12. rld613 Group Title
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    wasn't it d/dx(F(x)-F(17))

    • 2 years ago
  13. rld613 Group Title
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    oh i see where i went wrong!!!!

    • 2 years ago
  14. JamesJ Group Title
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    Yes, but F is not the integrand.

    • 2 years ago
  15. rld613 Group Title
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    F(x)=-cosx/x???

    • 2 years ago
  16. JamesJ Group Title
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    Nooo

    • 2 years ago
  17. rld613 Group Title
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    K just tell me the answer

    • 2 years ago
  18. JamesJ Group Title
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    Look at the ln example again.

    • 2 years ago
  19. rld613 Group Title
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    In the example we subsituted t for x

    • 2 years ago
  20. rld613 Group Title
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    In the example we subsituted t for x

    • 2 years ago
  21. JamesJ Group Title
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    \[ \frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt \]

    • 2 years ago
  22. JamesJ Group Title
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    What is the value of that expression?

    • 2 years ago
  23. rld613 Group Title
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    i dont know i am feeling very stupid!!!!!! dF/dx=ln(x^2+1)

    • 2 years ago
  24. JamesJ Group Title
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    If \[ F(t) = \int \ln(t^2+1) \ dt \] then \[ \int_2^x \ln(t^2+1) \ dt = F(x) - F(2) \]. Hence \[\frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt = \frac{d \ }{dx} (F(x) - F(2)) \]

    • 2 years ago
  25. rld613 Group Title
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    righ

    • 2 years ago
  26. JamesJ Group Title
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    and by the Fund Theorem of Calculus, dF/dx = ln(x^2 + 1). Also (d/dx)F(2) = 0 because F(2) is a number, a constant. Hence the entire expression is just ln(x^2+1)

    • 2 years ago
  27. missyfredtom Group Title
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    James do you think you help me please?

    • 2 years ago
  28. JamesJ Group Title
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    So, return now to the next example where the integrand has a sin function. What is the value of that derivative?

    • 2 years ago
  29. JamesJ Group Title
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    @mft, I'll try and get to it. unfortunately you're not the first to ask.

    • 2 years ago
  30. rld613 Group Title
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    dont take james away form me:(

    • 2 years ago
  31. missyfredtom Group Title
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    i can wait

    • 2 years ago
  32. JamesJ Group Title
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    quick rld613. I want to move on with you to yet another example afterwards

    • 2 years ago
  33. Hero Group Title
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    rld said she didn't need OS anymore

    • 2 years ago
  34. JamesJ Group Title
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    so (d/dx) int_17^x sin(t^2)/t dt = ...

    • 2 years ago
  35. rld613 Group Title
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    i didnt get that why is 17 to th epower of x

    • 2 years ago
  36. JamesJ Group Title
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    \[ (d/dx) \int_{17}^x \sin(t^2)/t \ dt \]

    • 2 years ago
  37. rld613 Group Title
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    yes

    • 2 years ago
  38. JamesJ Group Title
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    evaluate. What is the that equal to.

    • 2 years ago
  39. rld613 Group Title
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    y is it wrong what i showed u b4?

    • 2 years ago
  40. rld613 Group Title
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    plz be nice to me and show me all the step? :D

    • 2 years ago
  41. JamesJ Group Title
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    No. You write out the steps, following line by the line the example we just used for ln. I'm going to help someone else for a while and expect the right answer when I get back ;-)

    • 2 years ago
  42. rld613 Group Title
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    LOL see u later :D

    • 2 years ago
  43. JamesJ Group Title
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    I'm serious. And I'll be back in 5 minutes, so hurry.

    • 2 years ago
  44. JamesJ Group Title
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    ??

    • 2 years ago
  45. rld613 Group Title
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    u did u come back already!!!

    • 2 years ago
  46. JamesJ Group Title
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    What's the answer?

    • 2 years ago
  47. rld613 Group Title
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    K can u walk me thru the steps cuz like i bever learnt this stuff? YOu r so scary LOL

    • 2 years ago
  48. rld613 Group Title
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    I was hoping i wld have the answer b4 u wld return

    • 2 years ago
  49. rld613 Group Title
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    teh answer wld sinx/x?

    • 2 years ago
  50. JamesJ Group Title
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    Exactly as before, exactly, let \[ F(t) = \int \sin(t^2)/t \ dt \] Then \[ \int_{17}^x \sin(t^2)/t \ dt = F(x) - F(17) \] Thus the derivative of this definite integral \[ \frac{d\ }{dx} (F(x) - F(17)) = ... \]

    • 2 years ago
  51. rld613 Group Title
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    iSo what is F(x)?????

    • 2 years ago
  52. rld613 Group Title
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    That is where i am going wrong

    • 2 years ago
  53. rld613 Group Title
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    oh i know si(x)?

    • 2 years ago
  54. rld613 Group Title
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    d/dx(si(x)?

    • 2 years ago
  55. JamesJ Group Title
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    like we've seen, we actually don't need an explicit formula for F(x). We just need to know it is this integral and then use the Fundamental Theorem of Calculus.

    • 2 years ago
  56. JamesJ Group Title
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    What is dF/dx here? What is it equal to?

    • 2 years ago
  57. JamesJ Group Title
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    By the FTC, dF/dx = .... what?

    • 2 years ago
  58. rld613 Group Title
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    You are forsure ready to kill me!!!!!!!!!!!!!!!

    • 2 years ago
  59. rld613 Group Title
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    You are forsure ready to kill me!!!!!!!!!!!!!!!

    • 2 years ago
  60. Hero Group Title
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    shakes head

    • 2 years ago
  61. rld613 Group Title
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    dF/dx= sinx^2/x

    • 2 years ago
  62. JamesJ Group Title
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    correct. Hence the derivative wrt (with respect to) x of the entire integral equals what?

    • 2 years ago
  63. pokemon23 Group Title
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    hey james can you help me with math?

    • 2 years ago
  64. JamesJ Group Title
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    This thing ... what's it equal to?

    • 2 years ago
  65. rld613 Group Title
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    sinx^2/x????? this is a guess

    • 2 years ago
  66. JamesJ Group Title
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    it shouldn't be guess. it is exactly right.

    • 2 years ago
  67. rld613 Group Title
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    oh ya !!!!!!!!

    • 2 years ago
  68. rld613 Group Title
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    That is what i thought in the first place but i left out by accident the squared

    • 2 years ago
  69. rld613 Group Title
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    I can be so annoying sometimes

    • 2 years ago
  70. JamesJ Group Title
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    Now one more to make sure you really understand. Evaluate this: \[ \frac{d \ }{dx} \int_x^{x^2} \sqrt{t^3+1} \ dt \]

    • 2 years ago
  71. rld613 Group Title
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    oh u r so funny!!!

    • 2 years ago
  72. JamesJ Group Title
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    Now write out the steps. This problem isn't exactly the same as the others.

    • 2 years ago
  73. rld613 Group Title
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    ok give me a sec

    • 2 years ago
  74. rld613 Group Title
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    \[d/dx=(\sqrt{x ^{6}+1}-\sqrt{x ^{3}+1})\]

    • 2 years ago
  75. rld613 Group Title
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    This one i guessed

    • 2 years ago
  76. rld613 Group Title
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    I think it was suppossed to be dF/dx

    • 2 years ago
  77. JamesJ Group Title
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    The expression is equal to \[ \frac{d \ }{dx} \left( F(x^2) - F(x) \right) \ \ \ \ \ \ --(*)\] where by the Fund Theorem of Calculus, \[ dF/dx = \sqrt{x^3+1} \] Now given that, evaluate the first expression, (*).

    • 2 years ago
  78. JamesJ Group Title
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    hint: you need to use the chain rule.

    • 2 years ago
  79. rld613 Group Title
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    ok so let me try that

    • 2 years ago
  80. rld613 Group Title
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    james u gotta help me out on this one

    • 2 years ago
  81. JamesJ Group Title
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    you think about it for a bit and write the answer sometime in the next day when you know what's going on.

    • 2 years ago
  82. rld613 Group Title
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    alrighty thanks james

    • 2 years ago
  83. rld613 Group Title
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    I will call you back when i get the

    • 2 years ago
  84. rld613 Group Title
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    I got the answer :D

    • 2 years ago
  85. rld613 Group Title
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    \[2x \sqrt{x ^{6}+1} - \sqrt{x ^{3}+1}\] Here is my answer. Thanks james for your help. I really appreciate it

    • 2 years ago
  86. JamesJ Group Title
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    that's it. Good

    • 2 years ago
  87. JamesJ Group Title
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    One more variation they might throw at you in the exam. Evaluate: \[ \frac{d^2 \ }{dx^2} \int_2^x \ln(\cos t) \ dt \]

    • 2 years ago
  88. rld613 Group Title
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    Oh this is very simple there is just one small catch that you have to differentiate it twice

    • 2 years ago
  89. rld613 Group Title
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    d/dx(ln(cosx)) (1/cosx)*-sin(x)= -sin(x)/cos(x) -tan(x)

    • 2 years ago
  90. JamesJ Group Title
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    exactly, good.

    • 2 years ago
  91. rld613 Group Title
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    I think that is the answer. I took my final exam already and it was basically simple except ofr a related rates problem. Going on vacation for a month So see u then. Thanks for your help james

    • 2 years ago
  92. rld613 Group Title
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    oh u are here LOL

    • 2 years ago
  93. rld613 Group Title
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    Thanks for helping me out

    • 2 years ago
  94. JamesJ Group Title
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    sure. have a good vacation.

    • 2 years ago
  95. rld613 Group Title
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    U better take a vacation from OS tooo!!! :D

    • 2 years ago
  96. JamesJ Group Title
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    I might just do that.

    • 2 years ago
  97. rld613 Group Title
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    Ya u need a break to refresh again

    • 2 years ago
  98. rld613 Group Title
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    OS wldnt survive without James myinaya satellite and Hero

    • 2 years ago
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