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Ephilo

find the integral.

  • one year ago
  • one year ago

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  1. rosjua
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    -5^-x/(log(5))+C

    • one year ago
  2. Ephilo
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    |dw:1361280612277:dw|

    • one year ago
  3. mathsmind
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    i have been trying to enter the site since yesterday did you all have the same problem?

    • one year ago
  4. mathsmind
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    anyways there are many ways to solve this problem, one of them would be Taylor series the other one would be substitution method

    • one year ago
  5. Ephilo
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    @mathsmind yea ive been having problems with it to so i did the problems i know how to do until it finally works

    • one year ago
  6. Ephilo
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    @mathsmind i figured that one out im stuck on another one now

    • one year ago
  7. Ephilo
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    evaluate the intergal |dw:1361284859202:dw|

    • one year ago
  8. Ephilo
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    @mathsmind that one ^^^

    • one year ago
  9. mathsmind
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    sorry i meant i was having problems entering the website since yesterday

    • one year ago
  10. mathsmind
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    i know how to solve both integral in my head

    • one year ago
  11. Ephilo
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    @mathsmind how long are you going to be one today ?

    • one year ago
  12. mathsmind
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    it depends on my work, if i am busy or not

    • one year ago
  13. mathsmind
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    can you answer my question please?

    • one year ago
  14. mathsmind
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    were you able to log on to the site

    • one year ago
  15. Ephilo
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    @mathsmind which one ? lol

    • one year ago
  16. Ephilo
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    oh no i wasnt i answered it above

    • one year ago
  17. mathsmind
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    this website? openstudy

    • one year ago
  18. Ephilo
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    it wasnt loading

    • one year ago
  19. Ephilo
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    i felt like crying lol, with out this website i don't know what id do

    • one year ago
  20. mathsmind
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    ok let me reply to the last integral

    • one year ago
  21. mathsmind
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    the answer for the last integral would be pi/6

    • one year ago
  22. mathsmind
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    now by looking at the last integral you can find out from the table that it is equal to arcsin(x/2)

    • one year ago
  23. Ephilo
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    for the 4-x?

    • one year ago
  24. mathsmind
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    \[\int\limits_{0}^{1}\frac{ dx }{ \sqrt{4-x^2} }\]

    • one year ago
  25. mathsmind
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    is that the integral or not?

    • one year ago
  26. Ephilo
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    yepp

    • one year ago
  27. mathsmind
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    the answer is pi/6

    • one year ago
  28. Ephilo
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    how did you get it?

    • one year ago
  29. mathsmind
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    ok there are two ways to do that

    • one year ago
  30. mathsmind
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    one way is to look at the arctrigs integrals

    • one year ago
  31. mathsmind
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    you know the table of integrals right!

    • one year ago
  32. mathsmind
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    the other way is to go through full substitution method

    • one year ago
  33. Ephilo
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    lol no but ill look them up

    • one year ago
  34. mathsmind
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    ok do you want detailed solution then

    • one year ago
  35. Ephilo
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    the u sub thing ?

    • one year ago
  36. mathsmind
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    yep

    • one year ago
  37. mathsmind
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    you let x=2u

    • one year ago
  38. mathsmind
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    x^2 = 4u^2

    • one year ago
  39. Ephilo
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    okay i get it so far

    • one year ago
  40. mathsmind
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    can you differentiate the last bit?

    • one year ago
  41. mathsmind
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    dx = 2du

    • one year ago
  42. mathsmind
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    \[\int\limits_{0}^{1}\frac{ 2du }{\sqrt{4-4u^2} }\]

    • one year ago
  43. mathsmind
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    \[\int\limits\limits_{0}^{1}\frac{ du }{\sqrt{1-u^2} }\]

    • one year ago
  44. Ephilo
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    your a math genuis lol

    • one year ago
  45. mathsmind
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    thanks that was kind of you, and you are a bright student

    • one year ago
  46. mathsmind
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    let me give you a third way how to do that

    • one year ago
  47. Ephilo
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    i understand the u-sub the most

    • one year ago
  48. Ephilo
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    i have three more integral questions

    • one year ago
  49. mathsmind
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    ok go ahed

    • one year ago
  50. mathsmind
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    you need to know different methods to solve one problem , that for future note...

    • one year ago
  51. Ephilo
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    altho the differentiate part is a bit hard

    • one year ago
  52. mathsmind
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    i have a phone call but still submit your work

    • one year ago
  53. Ephilo
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    but ill look back it later because i have to get this course done to graduate

    • one year ago
  54. mathsmind
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    no i meant you make y =2sinx sub

    • one year ago
  55. mathsmind
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    different substitution

    • one year ago
  56. mathsmind
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    if you look at the unit triangle you can figure out that you need a sin sub

    • one year ago
  57. Ephilo
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    okay

    • one year ago
  58. Ephilo
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    find the intergal |dw:1361286908472:dw|

    • one year ago
  59. mathsmind
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    again you are going to get an arctan but now we need to look at the factors

    • one year ago
  60. mathsmind
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    just by looking at this integral we will get 4/3arctan(3x) +c

    • one year ago
  61. mathsmind
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    the question is what was x=? in this u sub

    • one year ago
  62. mathsmind
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    you need to assume that 3x=u, 9x^2=u^2, 3dx=du

    • one year ago
  63. mathsmind
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    \[\int\limits \frac{ 4du }{ 3(1+u^2) }=\frac{ 4 }{ 3}\arctan(u)+c\]

    • one year ago
  64. mathsmind
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    \[u=3x, \therefore \frac{ 4 }{ 3 }\arctan(3x)+c\]

    • one year ago
  65. mathsmind
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    that's your final answer

    • one year ago
  66. Ephilo
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    okay i just did the other one so i have one more integral question

    • one year ago
  67. Ephilo
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    |dw:1361287534741:dw|

    • one year ago
  68. mathsmind
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    ok

    • one year ago
  69. mathsmind
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    again you can see we will get the arctan + something

    • one year ago
  70. mathsmind
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    your answer should be\[\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2}(x-1))+c\]

    • one year ago
  71. mathsmind
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    \[\int\limits\limits\limits \frac{ dx }{4+(1-x)^2}\]

    • one year ago
  72. mathsmind
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    now 2u=1-x, 4u^2=(1-x)^2,

    • one year ago
  73. mathsmind
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    now one thing you need to know is how to let the 4 be a one in the denominator

    • one year ago
  74. Ephilo
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    how do i know that?

    • one year ago
  75. mathsmind
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    ok let me show, it is clear from the u-sub

    • one year ago
  76. mathsmind
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    remember that 2u =1-x, 2du=-dx

    • one year ago
  77. Ephilo
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    okay so far so good lol

    • one year ago
  78. mathsmind
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    \[\int\limits\frac{ 2du }{4(1+(u)^2)}\]

    • one year ago
  79. mathsmind
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    can you see it better this way?

    • one year ago
  80. mathsmind
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    \[\frac{ 1 }{ 2 }\arctan(u)+c\]

    • one year ago
  81. mathsmind
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    \[2u=1-x, \space u=\frac{ 1 }{ 2 }(1-x)\]

    • one year ago
  82. mathsmind
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    \[\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2 }(1-x))+c\]

    • one year ago
  83. mathsmind
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    that's your final answer

    • one year ago
  84. Ephilo
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    okay thanks ! im working on some ill let you know if i need more help

    • one year ago
  85. mathsmind
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    you don't sound like you got the last one?

    • one year ago
  86. Ephilo
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    lol i havent fully looked at it yet im finishing a problem

    • one year ago
  87. mathsmind
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    ok

    • one year ago
  88. mathsmind
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    so i read your mind well hehehe

    • one year ago
  89. Ephilo
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    lol yeahh i was wondering how you knew that,but im looking at it now

    • one year ago
  90. mathsmind
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    i still don't understand how the engagement scheme works on open study

    • one year ago
  91. Ephilo
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    i get that one

    • one year ago
  92. mathsmind
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    good

    • one year ago
  93. Ephilo
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    i think its by the questions you answer, and medals you receive

    • one year ago
  94. mathsmind
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    no i am not asking about those two, i am asking about the engagement part

    • one year ago
  95. mathsmind
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    the one that has learner next to it

    • one year ago
  96. Ephilo
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    lol i thinks its from asking questions cause thats how you learn right

    • one year ago
  97. Ephilo
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    okay i found two i need help on

    • one year ago
  98. mathsmind
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    go ahead

    • one year ago
  99. Ephilo
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    determine which of the integrals can be found using the basic integration formulas you have studied so far in the text.

    • one year ago
  100. mathsmind
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    i think you need to open a new thread because this one is getting heavy with BW

    • one year ago
  101. Ephilo
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    lol okay i will

    • one year ago
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