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1018

  • one year ago

integrate 1/x^1.005

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  1. UnkleRhaukus
    • one year ago
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    first write is as x ^ n

  2. UnkleRhaukus
    • one year ago
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    using 1 / x^m = x^-m

  3. 1018
    • one year ago
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    yes, x^-1.005. is this right?

  4. UnkleRhaukus
    • one year ago
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    good, so you have to integrate it now, (with respect to x, i'm assuming) \[\int x^{-1.005}\,\mathrm dx\] are you given limits or not?

  5. 1018
    • one year ago
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    yes dx and also i am given the limits, but i am wondering on how to integrate that first.

  6. 1018
    • one year ago
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    the limits arent necessary at this moment, am i correct? or is it?

  7. UnkleRhaukus
    • one year ago
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    the general case is \[\int x^n\,\mathrm dx = \frac{x^{n+1}}{n+1}+c\] for the indefinite integral and \[\int\limits_{x_i}^{x_f} x^n\,\mathrm dx = \left.\frac{x^{n+1}}{n+1}\right|_{x=x_i}^{x=x_f}\] for the definite integral

  8. UnkleRhaukus
    • one year ago
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    i remember it as: "add one to the index, and divide by the new index"

  9. 1018
    • one year ago
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    so the integration is the same before substituting the values of limits right?

  10. UnkleRhaukus
    • one year ago
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    yeah, pretty much

  11. 1018
    • one year ago
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    yeah, that's what i did, but in the solution i have here, it says its integral is -(200/x^0.005)

  12. 1018
    • one year ago
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    im confused by the 200

  13. UnkleRhaukus
    • one year ago
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    what did you get?

  14. 1018
    • one year ago
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    my answer is x^0.005/0.005

  15. UnkleRhaukus
    • one year ago
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    what is 1/0.005 equal to?

  16. 1018
    • one year ago
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    oh wait, is it because 0.005 is 1/200?

  17. UnkleRhaukus
    • one year ago
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    yes!

  18. 1018
    • one year ago
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    i just entered on the calcu. lol

  19. 1018
    • one year ago
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    yeah im having second thoughts lol. maybe the solution made the x the denominator again?

  20. 1018
    • one year ago
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    but now im confused where the negative came from. the answer is -(200/x^0.005)

  21. UnkleRhaukus
    • one year ago
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    x^(-1.005) x^(-0.005) / -0.005 = -200 x^(-0.005) = -200 / x^(0.005)

  22. 1018
    • one year ago
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    oh yes of course i forgot its -0.005 not 0.005. haha. hey thanks man, appreciate the help

  23. UnkleRhaukus
    • one year ago
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    if this is the indefinite integral (no limits) don't forget to +c

  24. 1018
    • one year ago
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    yup thanks again!

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