1 / 13

2414 Calculus II Chapter 10.3 Polar Derivatives and Area

2414 Calculus II Chapter 10.3 Polar Derivatives and Area. To find the slope of a polar curve:. We use the product rule here. Example:. Area Inside a Polar Graph:. The length of an arc (in a circle) is given by r . q when q is given in radians.

hera
Download Presentation

2414 Calculus II Chapter 10.3 Polar Derivatives and Area

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. 2414 Calculus IIChapter 10.3Polar Derivatives and Area

  2. To find the slope of a polar curve: We use the product rule here.

  3. Example:

  4. Area Inside a Polar Graph: The length of an arc (in a circle) is given by r.q when q is given in radians. For a very small q, the curve could be approximated by a straight line and the area could be found using the triangle formula:

  5. We can use this to find the area inside a polar graph.

  6. Example: Find the area enclosed by:

  7. Notes: To find the area between curves, subtract: Just like finding the areas between Cartesian curves, establish limits of integration where the curves cross.

  8. When finding area, negative values of r cancel out: Area of one leaf times 4: Area of four leaves:

  9. Review for Test 4 Rectangular Find Radius & Interval of Convergence

  10. Review for Test 4

  11. To find the length of a curve: Remember: For polar graphs: If we find derivatives and plug them into the formula, we (eventually) get: So:

  12. There is also a surface area equation similar to the others we are already familiar with: When rotated about the x-axis: p

More Related