M408M Learning Module Pages
Main page ## Chapter 10: Parametric Equations and Polar Coordinates## Learning module LM 10.1: Parametrized Curves:## Learning module LM 10.2: Calculus with Parametrized Curves:## Learning module LM 10.3: Polar Coordinates:## Learning module LM 10.4: Areas and Lengths of Polar Curves:Area inside a polar curveArea between polar curves Arc lengths of polar curves ## Learning module LM 10.5: Conic Sections:## Learning module LM 10.6: Conic Sections in Polar Coordinates:## Chapter 12: Vectors and the Geometry of Space## Chapter 13: Vector Functions## Chapter 14: Partial Derivatives## Chapter 15: Multiple Integrals |
## Area inside a polar curve
Now we can compute the area inside of polar curve $r=f(\theta)$
between angles $\theta=a$ and $\theta=b$. As with all bulk
quantities, we - Break the region into $N$ small pieces.
- Estimate the contribution of each piece.
- Add up the pieces.
- Take a limit to get an integral.
The following video goes over the derivation of this formula, and uses it to compute the area inside one lobe of a cardioid. |