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anonymous

  • one year ago

Medal** Please help Interchange the order of the integration and evaluate the integral

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  1. anonymous
    • one year ago
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    \[\int\limits_{0}^{pi}\int\limits_{\pi}^{\pi} \frac{ siny }{ y }dydx\]

  2. Astrophysics
    • one year ago
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    Are those the right intervals?

  3. anonymous
    • one year ago
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    yes

  4. Astrophysics
    • one year ago
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    Ok, think of it this way |dw:1436942548336:dw|

  5. anonymous
    • one year ago
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    oki...how do i change my limits

  6. Astrophysics
    • one year ago
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    Well we have to draw it out, but as it's continuous we can say \[\int\limits_{a}^{b} \int\limits_{c}^{d} f(x,y) dy dx = \int\limits_{c}^{d} \int\limits_{a}^{b} f(x,y) dxdy\]

  7. anonymous
    • one year ago
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    ok so my limits flip?

  8. Astrophysics
    • one year ago
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    Sec, I don't think it's continous

  9. Astrophysics
    • one year ago
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    |dw:1436943113232:dw| this is how your graph would like right

  10. anonymous
    • one year ago
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    yes it would

  11. Astrophysics
    • one year ago
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    Ok, so now that should be easy to interchange, |dw:1436943501108:dw|

  12. anonymous
    • one year ago
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    only my second integral changes right?

  13. Astrophysics
    • one year ago
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    Well, we should get \[\int\limits_{0}^{\pi} \int\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

  14. anonymous
    • one year ago
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    why isnt it o to x?

  15. anonymous
    • one year ago
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    i thought it would be from x to pi

  16. Astrophysics
    • one year ago
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    Notice how x is horizontal, also it wouldn't make sense when you are integrating to have x after right?

  17. anonymous
    • one year ago
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    right because its dy dx

  18. Astrophysics
    • one year ago
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    I'm a bit skeptical about the graph mhm

  19. Astrophysics
    • one year ago
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    Maybe I'm just a bit tired haha, well does it look good to you?

  20. anonymous
    • one year ago
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    i understand what your doing

  21. anonymous
    • one year ago
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    i would intregate siny/y from o to y first?

  22. Astrophysics
    • one year ago
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    Yup

  23. anonymous
    • one year ago
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    would i do quotient rule to intregrate?

  24. Astrophysics
    • one year ago
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    What do you mean?

  25. Astrophysics
    • one year ago
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    Like derivatives?

  26. anonymous
    • one year ago
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    yeah im a bit confused on how to integrate siny/y

  27. Astrophysics
    • one year ago
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    No, remember we are integrating respect to x, so we treat siny/y as a constant

  28. Astrophysics
    • one year ago
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    I'm still skeptical about the graph, it's throwing me off, and I'm a bit tired to confirm I'm going to tag the illustrious @ganeshie8 to confirm

  29. anonymous
    • one year ago
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    ok thank you...

  30. Astrophysics
    • one year ago
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    |dw:1436944319331:dw|

  31. ganeshie8
    • one year ago
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    \[\int\limits_{\pi}^{\pi}f(x)\,dx = 0\] am i missing somthing here ?

  32. Astrophysics
    • one year ago
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    Yeah, exactly, but I wasn't really sure whether the interchange should make a difference or not

  33. ganeshie8
    • one year ago
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    it shouldn't because we must get the same answer either way

  34. anonymous
    • one year ago
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    are the limits 0 to y. correct then?

  35. Astrophysics
    • one year ago
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    No the limits are wrong, I knew it...something seemed fishy

  36. anonymous
    • one year ago
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    how to find them? drawing again?

  37. anonymous
    • one year ago
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    would it be pi to x?

  38. ganeshie8
    • one year ago
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    The problem itself is messed up, please double check the limits in original question

  39. anonymous
    • one year ago
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    i just checked again...those are th limits given in the practice test

  40. Astrophysics
    • one year ago
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    \[\int\limits\limits_{0}^{\pi} \int\limits\limits_{x}^{\pi}\] my drawing is for this

  41. ganeshie8
    • one year ago
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    as you can see the original integral, as-it-is, evaluates to 0. end of story. take a screenshot and attach if you want to further debug for a possible typo..

  42. Astrophysics
    • one year ago
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    Yeah this problem is a bit weird lol

  43. anonymous
    • one year ago
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    1 Attachment
  44. ganeshie8
    • one year ago
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    because both \(x\) and \(\pi\) look alike typographically

  45. anonymous
    • one year ago
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    the first question

  46. Astrophysics
    • one year ago
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    Mine works if you have an x, I'm going to stick with it being x haha, the other does not make sense, now I think that is an x instead of pi.

  47. anonymous
    • one year ago
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    hmm oki lets go with x...since pi to pi doesnt make sense

  48. ganeshie8
    • one year ago
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    yeah i think thats the best we can do

  49. Astrophysics
    • one year ago
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    Yeah lets treat it like x, you'll learn this way to I guess

  50. Astrophysics
    • one year ago
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    |dw:1436944946903:dw|

  51. anonymous
    • one year ago
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    alright so our new limits would be in respect to the drawing

  52. Astrophysics
    • one year ago
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    So go ahead and integrate what we originally had

  53. Astrophysics
    • one year ago
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    \[\large \int\limits\limits_{0}^{\pi} \int\limits\limits_{0}^{y} \frac{ \sin y }{ y } dx dy\]

  54. anonymous
    • one year ago
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    siny/y changes to siny/y *y= siny?

  55. Astrophysics
    • one year ago
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    Mhm?

  56. anonymous
    • one year ago
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    i got 1 for the first integration

  57. ganeshie8
    • one year ago
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    \[\large \int\limits_{0}^{\pi}\int\limits_{x}^{\pi} \frac{ \sin y }{ y }\,dydx = \int\limits_{0}^{\pi}\int\limits_{0}^{y} \frac{ \sin y }{ y }\,dxdy = \int\limits_0^{\pi} \frac{\sin y}{y}*y \,dy = -2\]

  58. anonymous
    • one year ago
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    not just 2?

  59. Astrophysics
    • one year ago
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    |dw:1436945173549:dw|

  60. Astrophysics
    • one year ago
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    Make sense?

  61. anonymous
    • one year ago
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    yes thank you so much!

  62. Astrophysics
    • one year ago
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    and that should = 2 as ganeshie showed

  63. ganeshie8
    • one year ago
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    Ahh right, my mistake, it should be +2

  64. Astrophysics
    • one year ago
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    Yeah haha

  65. anonymous
    • one year ago
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    wow thank you so much you guys!

  66. Astrophysics
    • one year ago
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    Np, you can finish it off right to get 2?

  67. anonymous
    • one year ago
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    yes :)

  68. Astrophysics
    • one year ago
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    Ok cool

  69. Astrophysics
    • one year ago
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    Yeah about earlier, the question wasn't really making sense to me, because when we have such integrals \[\int\limits_{x}^{x} dx = 0\] it makes sense right using FTC

  70. anonymous
    • one year ago
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    yes i agree

  71. Astrophysics
    • one year ago
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    Alright cool, good luck on your exam :)

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