Integration By Parts
Arc Length of a Curve
Objectives
- Determine the length of a curve, \(y=f(x)\), between two points.
- Determine the length of a curve, \(x=g(y)\) , between two points
Summary
The arc length,\(L\),along the curve \(y = f(x)\) from \(x = a\) to \(x = b\) is given by $$(L =\int_{a}^{b} \sqrt{1+f'(x)^2} dx$$
The arc length,\(L\),along the curve \(x = g(y)\) from \(y = c\) to \(x = d\) is given by $$L =\int_{c}^{d} \sqrt{1+g'(y)^2} dy$$