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Jonask

integration- radicals

  • one year ago
  • one year ago

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  1. Kanwar245
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    ?

    • one year ago
  2. Jonask
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    \[\color{blue}{\huge\int_0^1\sqrt[3]{1-x^7}-\sqrt[7]{1-x^3}dx}\]

    • one year ago
  3. UnkleRhaukus
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    \[\color{blue}{\int_0^1\sqrt[3]{1-x^7}dx-\int\sqrt[7]{1-x^3}dx}\]

    • one year ago
  4. Jonask
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    yes but when i do that it still seems ugly

    • one year ago
  5. UnkleRhaukus
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    do one half at a time

    • one year ago
  6. Jonask
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    i shud make a u sub \[u=1-x^7\]

    • one year ago
  7. Jonask
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    in the 1st one

    • one year ago
  8. UnkleRhaukus
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    i'd say so

    • one year ago
  9. Jonask
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    \[u=1-x^7\] \[\int\frac{u^{1/3}}{7x^6}du\]

    • one year ago
  10. Jonask
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    the x^6 is a problem

    • one year ago
  11. Jonask
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    \[\int\frac{u^{1/3}}{7(1-u)^{1/7}}\]

    • one year ago
  12. UnkleRhaukus
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    hmm,

    • one year ago
  13. UnkleRhaukus
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    maybe that method isn't going to work

    • one year ago
  14. Jonask
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    http://www.wolframalpha.com/input/?i=integral+%281-x%5E7%29%5E%7B1%2F3%7D-%281-x%5E3%29%5E%7B1%2F7%7D ugly as well but i think we are supposed to use 'by parts'

    • one year ago
  15. UnkleRhaukus
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    where did you get this question?

    • one year ago
  16. Jonask
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    steward calculus advanved problem

    • one year ago
  17. Jonask
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    *

    • one year ago
  18. shubhamsrg
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    what if we use the property integral ( f(x) from x=a to b = f(a+b-x) from x= a to b )?

    • one year ago
  19. Jonask
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    in this case a+b=0+1 int f(1-x)=f(x)

    • one year ago
  20. shubhamsrg
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    yep, am not too sure if that'll work though, but probably should work ?

    • one year ago
  21. Jonask
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    ok i have to go i;ll try it thanks to everyone for the effort

    • one year ago
  22. SithsAndGiggles
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    According to WA, the definite integral is 0: http://www.wolframalpha.com/input/?i=integrate+%28%281-x%5E7%29%5E%281%2F3%29+-+%281-x%5E3%29%5E%281%2F7%29%29+over+%5B0%2C1%5D Maybe there's some detail we're not getting about the function itself.

    • one year ago
  23. Jonask
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    interesting result maybe this property is because of the function is actually an inverse of itself i mean \[f(x)=\sqrt[3]{1-x^7}\] then \[f^{-1}(x)=\sqrt[7]{1-x^3}\] should this mean anything

    • one year ago
  24. Jonask
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    \[\int_0^1 f(x)-f^{-1}(x) \space dx\] \[f(1)=f^{-1}(1)=0\]

    • one year ago
  25. experimentX
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    this is a famous question on M.SE

    • one year ago
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