Question

How do you find the arc length of the curve `x=y+y^3` over the interval [1,4]?

Answer 1

I used WolframAlpha to do the integration:
`L = int_1^4 sqrt(1 + (1 + 3y^2)^2)dy = 66.1093`

Explanation:

From the reference Arc Length

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

`dx/dy = 1 + 3y^2`

`L = int_1^4 sqrt(1 + (1 + 3y^2)^2)dy`