Question

Calculus 2: Arc Length help please. y=(1/12x^3)+(1/x), limit 0 to 2, however do not need to substitute in limits to equation. Thank you :).

Answer 1

\[1/12x^3-1/x\]

Answer 2

above statement should be + 1/x, sorry.
I've only managed to take the derivative of y' = 1/4x^2 + 1/x^2

Answer 3

arc length is
\[ \int \sqrt{1+(y')^2} \ dx \]
you should find
\[ y'= \frac{x^2}{4} - \frac{1}{x^2} \]
notice you should get a minus sign when you find the derivative of x^(-1)

the next step is to square that result (I assume you can do that?)
then add 1
then take the square root.
(In this problem, you get a perfect square, so it works out nicely)

Answer 4

However, if we try to evaluate the integral we will get an infinite result