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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.

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2414 Calculus II Chapter 10.3 Polar Derivatives and Area

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  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

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