Posted by **Rob** on Tuesday, December 4, 2007 at 2:44am.

For a smal change in x, dx:

ds² = dx² + dy²

ds = sqrt [(dx² + dy²)]

s = INTEGRAL of sqrt [(dx² + dy²)]

s = INTEGRAL of sqrt [(dx² + dy² * dx²/dx²)]

s = INTEGRAL of sqrt[(1 + dy² * 1/dx²)] dx

s = INTEGRAL of sqrt[(1 + (dy/dx)²)] dx

- Is this how you derive the formula for arc length? -
**drwls**, Tuesday, December 4, 2007 at 8:13am
Yes; that is one way.

- Is this how you derive the formula for arc length? -
**Matt**, Tuesday, December 4, 2007 at 11:09am
in the third step, how did you integrate the right side with no delta-variable?

- Is this how you derive the formula for arc length? -
**drwls**, Tuesday, December 4, 2007 at 11:12am
There is a delta variable dx. You must compute and insert dy/dx into the integrand to get the resulting arc length

## Answer This Question

## Related Questions

- CALCULUS 2!!! PLEASE HELP!! - I'm having trouble with this question on arc ...
- Calculus - Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t...
- calc check: curve length - Find the length of the curve y=(1/(x^2)) from ( 1, 1...
- calc: arc length - find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x...
- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- calculus - Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 ...
- ap calculus - Which of the following definite integrals gives the length of y = ...
- Calculus - I know how to do this problem, but I'm stuck at the arc length ...
- Calculus - Evaluate the indefinite integral: 8x-x^2. I got this but I the ...
- calc check: average value - Find the average value of the function "f(x) = x^2 ...

More Related Questions