1018
  • 1018
integrate 1/x^1.005
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnkleRhaukus
  • UnkleRhaukus
first write is as x ^ n
UnkleRhaukus
  • UnkleRhaukus
using 1 / x^m = x^-m
1018
  • 1018
yes, x^-1.005. is this right?

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UnkleRhaukus
  • UnkleRhaukus
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?
1018
  • 1018
yes dx and also i am given the limits, but i am wondering on how to integrate that first.
1018
  • 1018
the limits arent necessary at this moment, am i correct? or is it?
UnkleRhaukus
  • UnkleRhaukus
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
UnkleRhaukus
  • UnkleRhaukus
i remember it as: "add one to the index, and divide by the new index"
1018
  • 1018
so the integration is the same before substituting the values of limits right?
UnkleRhaukus
  • UnkleRhaukus
yeah, pretty much
1018
  • 1018
yeah, that's what i did, but in the solution i have here, it says its integral is -(200/x^0.005)
1018
  • 1018
im confused by the 200
UnkleRhaukus
  • UnkleRhaukus
what did you get?
1018
  • 1018
my answer is x^0.005/0.005
UnkleRhaukus
  • UnkleRhaukus
what is 1/0.005 equal to?
1018
  • 1018
oh wait, is it because 0.005 is 1/200?
UnkleRhaukus
  • UnkleRhaukus
yes!
1018
  • 1018
i just entered on the calcu. lol
1018
  • 1018
yeah im having second thoughts lol. maybe the solution made the x the denominator again?
1018
  • 1018
but now im confused where the negative came from. the answer is -(200/x^0.005)
UnkleRhaukus
  • UnkleRhaukus
x^(-1.005) x^(-0.005) / -0.005 = -200 x^(-0.005) = -200 / x^(0.005)
1018
  • 1018
oh yes of course i forgot its -0.005 not 0.005. haha. hey thanks man, appreciate the help
UnkleRhaukus
  • UnkleRhaukus
if this is the indefinite integral (no limits) don't forget to +c
1018
  • 1018
yup thanks again!

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