Area Approximation for Polar Plot
Area Approximation for Polar Plot
This Demonstration shows how the area bounded by a polar curve and two radial lines to can be approximated by summing the areas of sectors. The radii of the sectors can be based on midpoints, endpoints or random points. Select the checkbox to see the actual region being approximated. The area is approximated by Δ. As , with all →0, the area approaches the integral dθ.
r=f(θ)
θ=α
θ=β
1
2
n
∑
k=1
2
[f()]
θ
k
θ
k
n→∞
Δθ
k
1
2
β
∫
α
2
[f(θ)]