1 / 8

10.5 Area and Arc Length in Polar Coordinates

10.5 Area and Arc Length in Polar Coordinates. Miss Battaglia AP Calculus. Area in Polar Coordinates. If f is continuous and nonnegative on the interval [α,β], 0 < β – α < 2π, then the area of the region bounded by the graph of r=f( θ ) between the radial lines θ = α and θ =β is given by.

thanos
Download Presentation

10.5 Area and Arc Length in Polar Coordinates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 10.5 Area and Arc Length in Polar Coordinates Miss Battaglia AP Calculus

  2. Area in Polar Coordinates If f is continuous and nonnegative on the interval [α,β], 0 < β – α < 2π, then the area of the region bounded by the graph of r=f(θ) between the radial lines θ=α and θ=β is given by

  3. Proof of Area Remember the area of a sector is given by ½θr2 Radius of ith sector = f(θi) Central angle of ith sector = (β – α)/n = Δθ Taking the limit as n  ∞ produces

  4. Find the area enclosed by one loop of r=sin(4θ)

  5. Arc Length of a Polar Curve Let f be a function whose derivative is continuous on an intervalα <θ< β. The length of the graph of r=f(θ) from θ=α to θ=β is (Proof is Exercise 89 Section 10.5)

  6. Find the arc length from θ=0 to θ=2π for the cardioid r=f(θ)=2-2cosθ

  7. Classwork 1. Find the area of one petal of the rose curve given by r=3cos(3θ) 2. Find the arc length from θ=0 to θ=π for the cardioid r=f(θ)=sin2(θ/2)

  8. Homework • Read 10.5 Page 715 #1, 4, 7, 9, 11, 13, 25

More Related