anonymous 3 years ago calculus !!! help.

1. anonymous

If n is a known positive integer, for what value of K is $\int\limits_{1}^{k}x ^{n-1}dx=\frac{ 1 }{ n }$ ?

2. 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 $$\dfrac{1}{n}$$

3. zepdrix

Opps i made a boo boo, one sec.

4. zepdrix

$\large \frac{1}{n}\left(k^n-1^n\right)$When does THIS equal $$\dfrac{1}{n}$$

5. zepdrix

hmm

6. anonymous

ahhh i get it now! Thank you. you are always so helpful!

7. anonymous

I will go ahead and post the next question then. :)

8. zepdrix

Did you figure this one out? I'm having a brain fart on the last part here lol.