Polar Area & Arc Length Approximations

Ron Smith
1. Enter a function f(θ) such as θ, 1+2cos(θ), or 4sin(3θ) to see the graph of r = f(θ) 0 ≤ θ ≤ 2π. 2. Click "Partition" to see the lines that partition the angles α ≤ θ ≤ β into n equal angles. 3. Click "Sample" to see sample points, one in each angle of the partition. 4. Click "Sectors" to see the sectors approximating the area in each angle of the partition, as well as the approximating sum. 5. Click "Segments" to see the line segments between partition points and the approximating sum for the arc length.