Question

How do you set up an integral from the length of the curve `y=1/x, 1<=x<=5`?

Answer 1

`int_1^5sqrt(1+1/x^4)`

Explanation:

The length of the curve of `y` on `alt=xlt=b` is equal to:

`L=int_a^bsqrt(1+(dy/dx)^2)`

For `y=1/x`, we see that `y=x^-1` so `dy/dx=-x^-2=-1/x^2`. Then:

`L=int_1^5sqrt(1+(-1/x^2)^2)=int_1^5sqrt(1+1/x^4)`

Which can be plugged into a calculator for a result of `4.15145`.