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xartaan

Integral help, how to approach this?

  • one year ago
  • one year ago

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  1. xartaan
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    \[\int\limits_{0}^{1} \sin(y)(e-e^{y^{1/3} })dy\] is the integral. I can plug it into wolfram alpha and get a value, but I would like to know what steps get me there>

    • one year ago
  2. abb0t
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    Wow. That's an interesting integral. I would suggest distributing the sine function across and take the integral sepearately. e is constant so you can just factor that out. For the second integral, it gets a bit difficult. You could try and work with integration by parts twice.

    • one year ago
  3. calmat01
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    Except that the product of siny and e^y^1/3 is elliptic. Neither of those will differentiate to zero.

    • one year ago
  4. xartaan
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    Heh, I have a whole homework sheet of these iterated integrals that the inner integral isnt bad, but the insides are just impossible. WA wont even give steps, just values when I include the bounds.. Arg

    • one year ago
  5. calmat01
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    That is one hairy integral!

    • one year ago
  6. siddarth95
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    have you tried considering y^(1/3) as u ?

    • one year ago
  7. abb0t
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    I don't think you can use u-sub, since you don't have a du to substitute. But, I think since the integral is from 0<y<1 so it might be easier to just use the bounds given to evaluate. In theory, I think you can use series to solve this.

    • one year ago
  8. mathsmind
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    i would use taylor series to solve this problem

    • one year ago
  9. abb0t
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    Not series to solve the whole integral! Omg.

    • one year ago
  10. mathsmind
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    i used taylor's expansion and i got 0.1644

    • one year ago
  11. mathsmind
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    unless u want to use integration by parts and the Jacobin and polar coordinate,

    • one year ago
  12. mathsmind
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    to solve this problem

    • one year ago
  13. abb0t
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    Well, depending on the course this is being taught in, which is probably a Calc BC (II) course, I would suggest parts. However, if this was for ODE, then I might suggest using poolar coordinates or series expansion.

    • one year ago
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