Chap10_Sec4

Chap10_Sec4 - PARAMETRIC EQUATIONS & POLAR COORDINATES 10.4...

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10.4 Areas and Lengths in Polar Coordinates In this section, we will: Develop the formula for the area of a region whose boundary is given by a polar equation. PARAMETRIC EQUATIONS & POLAR COORDINATES
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AREAS IN POLAR COORDINATES We need to use the formula for the area of a sector of a circle A = ½ r 2 θ where: r is the radius. θ is the radian measure of the central angle. Formula 1
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AREAS IN POLAR COORDINATES Let R be the region bounded by the polar curve r = f ( θ ) and by the rays θ = a and θ = b, where: f is a positive continuous function. 0 < b – a 2 π Formula 3 is often written as with the understanding that r = f ( θ ). Note the similarity between Formulas 1 and 4. Formula 4
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In general, let R be a region that is bounded by curves with polar equations r = f ( θ ), r = g ( θ ), θ = a , θ = b , where: f ( θ ) g ( θ ) 0 0 < b – a < 2 π The area A of R is found by subtracting the area inside r = g ( θ ) from the area inside r = f ( θ ).
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This note was uploaded on 02/23/2010 for the course MATH 221 taught by Professor Staff during the Spring '08 term at Tulane.

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Chap10_Sec4 - PARAMETRIC EQUATIONS & POLAR COORDINATES 10.4...

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