Category:Arc Length of Curve in Polar Coordinates
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This category contains pages concerning Arc Length of Curve in Polar Coordinates:
Let $C$ be a curve embedded in a polar plane.
As a Function of Radial Coordinate
Let the angular coordinate $\theta$ of $C$ be defined as a function of the radial coordinate $r$:
- $\theta = \map f r$
The arc length $s$ of $C$ between $r = u$ and $r = v$ is defined as:
- $\ds s := \int_u^v \paren {\sqrt {1 + r^2 \paren {\frac {\d \theta} {\d r} }^2} } \rd r$
As a Function of Angular Coordinate
Let the radial coordinate $r$ of $C$ be defined as a function of the angular coordinate $\theta$:
- $r = \map f \theta$
The arc length $s$ of $C$ between $\theta = \alpha$ and $\theta = \beta$ is defined as:
- $\ds s := \int_\alpha^\beta \paren {\sqrt {\paren {\frac {\d r} {\d \theta} }^2 + r^2} } \rd \theta$
Pages in category "Arc Length of Curve in Polar Coordinates"
The following 5 pages are in this category, out of 5 total.