The discussion revolves around finding the arc length of a circle in the first quadrant, specifically for the equation x² + y² = a². Participants are exploring the integral for arc length, which is expressed as ∫ √(1 + (dy/dx)²) dx.
Participants are actively engaging with the problem, with some providing insights into their attempts and others prompting for further clarification on the integral. There is no explicit consensus, but guidance has been offered regarding potential methods to simplify the integral.
Some participants express uncertainty about the integral they have derived and mention not having used trigonometric substitution, which is suggested as a possible approach to move forward.
Well, show us where you got stuck.adi adi said:Homework Statement
find the arc length of a circle in the first quadrant with an equation x2 + y2 = a2
Homework Equations
arc length = ∫ √(1 + (dy/dx)2) dx
The Attempt at a Solution
i got stuck on how to solve the integral
yeah, i make the circle equation into y= √(a2-x2) , and then put it into the arc length equation.SteamKing said:Well, show us where you got stuck.
Did you calculate dy/dx for the arc of the circle, using its equation?
first i derive my y=√(a2-x2) into y'= - x/√(a2-x2)mfb said:You still didn't show the integral you want to solve and how you got it.
Did you try the usual trigonometric substitutions?
Then you should try that (after simplifying the expression a bit).adi adi said:and i didnt use trigonometric substitution