anonymous
  • anonymous
calculus !!! help.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
If n is a known positive integer, for what value of K is \[\int\limits_{1}^{k}x ^{n-1}dx=\frac{ 1 }{ n }\] ?
zepdrix
  • zepdrix
So let's just start from scratch, I'll bet we can figure this out. \[\large \int\limits_1^k x^{n-1}dx\]Taking the integral gives us,\[\huge \frac{1}{n}x^n|_1^k\] Evaluated at k and 1 gives us (I'm factoring the 1/n out first),\[\large \color{purple}{\frac{1}{n}\left(k-1\right)}\] And they're asking, When does \(\color{purple}{\textbf{this}}\) equal \(\dfrac{1}{n}\)
zepdrix
  • zepdrix
Opps i made a boo boo, one sec.

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zepdrix
  • zepdrix
\[\large \frac{1}{n}\left(k^n-1^n\right)\]When does THIS equal \(\dfrac{1}{n}\)
zepdrix
  • zepdrix
hmm
anonymous
  • anonymous
ahhh i get it now! Thank you. you are always so helpful!
anonymous
  • anonymous
I will go ahead and post the next question then. :)
zepdrix
  • zepdrix
Did you figure this one out? I'm having a brain fart on the last part here lol.

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