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rld613

  • 3 years ago

James?

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  1. neverforgetvivistee
    • 3 years ago
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    give me edals

  2. JamesJ
    • 3 years ago
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    so the answer is?

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

  4. neverforgetvivistee
    • 3 years ago
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    give me medals free medals for everyone

  5. rld613
    • 3 years ago
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    can you write the equation again please :D

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

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

  8. JamesJ
    • 3 years ago
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    No

  9. rld613
    • 3 years ago
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    where did i go wrong?

  10. JamesJ
    • 3 years ago
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    look at the earlier example with ln

  11. rld613
    • 3 years ago
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    k i will

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

  13. rld613
    • 3 years ago
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    oh i see where i went wrong!!!!

  14. JamesJ
    • 3 years ago
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    Yes, but F is not the integrand.

  15. rld613
    • 3 years ago
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    F(x)=-cosx/x???

  16. JamesJ
    • 3 years ago
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    Nooo

  17. rld613
    • 3 years ago
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    K just tell me the answer

  18. JamesJ
    • 3 years ago
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    Look at the ln example again.

  19. rld613
    • 3 years ago
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    In the example we subsituted t for x

  20. rld613
    • 3 years ago
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    In the example we subsituted t for x

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

  22. JamesJ
    • 3 years ago
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    What is the value of that expression?

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

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

  25. rld613
    • 3 years ago
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    righ

  26. JamesJ
    • 3 years ago
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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)

  27. missyfredtom
    • 3 years ago
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    James do you think you help me please?

  28. JamesJ
    • 3 years ago
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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?

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

  30. rld613
    • 3 years ago
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    dont take james away form me:(

  31. missyfredtom
    • 3 years ago
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    i can wait

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

  33. Hero
    • 3 years ago
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    rld said she didn't need OS anymore

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

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

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

  37. rld613
    • 3 years ago
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    yes

  38. JamesJ
    • 3 years ago
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    evaluate. What is the that equal to.

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

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

  41. JamesJ
    • 3 years ago
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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 ;-)

  42. rld613
    • 3 years ago
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    LOL see u later :D

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

  44. JamesJ
    • 3 years ago
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    ??

  45. rld613
    • 3 years ago
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    u did u come back already!!!

  46. JamesJ
    • 3 years ago
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    What's the answer?

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

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

  49. rld613
    • 3 years ago
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    teh answer wld sinx/x?

  50. JamesJ
    • 3 years ago
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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 \[ \frac{d\ }{dx} (F(x) - F(17)) = ... \]

  51. rld613
    • 3 years ago
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    iSo what is F(x)?????

  52. rld613
    • 3 years ago
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    That is where i am going wrong

  53. rld613
    • 3 years ago
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    oh i know si(x)?

  54. rld613
    • 3 years ago
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    d/dx(si(x)?

  55. JamesJ
    • 3 years ago
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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.

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

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

  58. rld613
    • 3 years ago
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    You are forsure ready to kill me!!!!!!!!!!!!!!!

  59. rld613
    • 3 years ago
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    You are forsure ready to kill me!!!!!!!!!!!!!!!

  60. Hero
    • 3 years ago
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    shakes head

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

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

  63. pokemon23
    • 3 years ago
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    hey james can you help me with math?

  64. JamesJ
    • 3 years ago
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    This thing ... what's it equal to?

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

  66. JamesJ
    • 3 years ago
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    it shouldn't be guess. it is exactly right.

  67. rld613
    • 3 years ago
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    oh ya !!!!!!!!

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

  69. rld613
    • 3 years ago
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    I can be so annoying sometimes

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

  71. rld613
    • 3 years ago
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    oh u r so funny!!!

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

  73. rld613
    • 3 years ago
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    ok give me a sec

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

  75. rld613
    • 3 years ago
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    This one i guessed

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

  77. JamesJ
    • 3 years ago
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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, (*).

  78. JamesJ
    • 3 years ago
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    hint: you need to use the chain rule.

  79. rld613
    • 3 years ago
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    ok so let me try that

  80. rld613
    • 3 years ago
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    james u gotta help me out on this one

  81. JamesJ
    • 3 years ago
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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.

  82. rld613
    • 3 years ago
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    alrighty thanks james

  83. rld613
    • 3 years ago
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    I will call you back when i get the

  84. rld613
    • 3 years ago
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    I got the answer :D

  85. rld613
    • 3 years ago
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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

  86. JamesJ
    • 3 years ago
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    that's it. Good

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

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

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

  90. JamesJ
    • 3 years ago
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    exactly, good.

  91. rld613
    • 3 years ago
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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

  92. rld613
    • 3 years ago
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    oh u are here LOL

  93. rld613
    • 3 years ago
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    Thanks for helping me out

  94. JamesJ
    • 3 years ago
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    sure. have a good vacation.

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

  96. JamesJ
    • 3 years ago
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    I might just do that.

  97. rld613
    • 3 years ago
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    Ya u need a break to refresh again

  98. rld613
    • 3 years ago
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    OS wldnt survive without James myinaya satellite and Hero

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