If n is a known positive integer, for what value of k is ... (see equation)

Question

saifoo.khan · Answer

k = constant.

anonymous · Answer

$$\int\limits_{1}^{k}x^n-1 dxugh it is  = 1/n$$
ugh it is supposed to be x^(n-1)

anonymous · Answer

Shall we work on this together?

anonymous · Answer

sure

anonymous · Answer

$$\int\limits_{1}^{k}(x^n-1)dx = 1/n?$$

anonymous · Answer

so if I understand correctly you're integrating from 1 to k for x to the power of n-1 with respect to x, and that is equal to 1/n, is that correct?

anonymous · Answer

yes!

anonymous · Answer

okay, so let's evaluate the integral on the left side, it should be (1/n)*x^n, from 1 to k right?

anonymous · Answer

yes.  and that is as far as I got.

anonymous · Answer

okay so we can divide out the 1/n from both sides, so now we have x^n from 1 to k is equal to 1, with me so far?

anonymous · Answer

yep

anonymous · Answer

okay so let's evaluate the integral of x^n from 1 to k, this equals k^n - 1^n

anonymous · Answer

1^n is just 1, so let's add 1 to both sides, now we have k^n = 2, so k is equal to the nth root of 2

anonymous · Answer

thanks!

anonymous · Answer

Since n has to be a positive integer, the only n that works is 1, which means k = 2

anonymous · Answer

the answer choices only go as far as the previous step