Arc Length Circle Quadrant 1: Solve ∫√(1+(dy/dx)2)dx

[adi adi]

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

 

[SteamKing]

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

Well, show us where you got stuck.

Did you calculate dy/dx for the arc of the circle, using its equation?

 

[adi adi]

Well, show us where you got stuck.

Did you calculate dy/dx for the arc of the circle, using its equation?

yeah, i make the circle equation into y= √(a²-x²) , and then put it into the arc length equation.
the problem is i can't solve my integral equation.

 

[mfb]

You still didn't show the integral you want to solve and how you got it.

Did you try the usual trigonometric substitutions?

 

[adi adi]

You still didn't show the integral you want to solve and how you got it.

Did you try the usual trigonometric substitutions?

first i derive my y=√(a²-x²) into y'= - x/√(a²-x²)
and then put it into arc length equation = ∫ √(1+(dy/dx)²) dx
resulting ∫ √(1+(- x/√(a²-x²))²) dx
and i got stuck there. i don't know how to solve my equation, and i didnt use trigonometric substitution

 

[mfb]

and i didnt use trigonometric substitution

Then you should try that (after simplifying the expression a bit).