Question

calculus !!! help.

Answer 1

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

Answer 2

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 \(\dfrac{1}{n}\)

Answer 3

Opps i made a boo boo, one sec.

Answer 4

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

Answer 5

hmm

Answer 6

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

Answer 7

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

Answer 8

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