How do you find the arc length of the curve x=y+y^3x=y+y3 over the interval [1,4]?

1 Answer
Douglas K.
Nov 1, 2016

I used WolframAlpha to do the integration:
L = int_1^4 sqrt(1 + (1 + 3y^2)^2)dy = 66.1093L=∫41√1+(1+3y2)2dy=66.1093

Explanation:

From the reference Arc Length

L = int_a^b sqrt(1 + (dx/dy)^2)dyL=∫ba√1+(dxdy)2dy

dx/dy = 1 + 3y^2dxdy=1+3y2

L = int_1^4 sqrt(1 + (1 + 3y^2)^2)dyL=∫41√1+(1+3y2)2dy

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