Lecture 13-4 - 13.4 - Double Integrals in Polar Form Recall...

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13.4 - Double Integrals in Polar Form Recall Consider ZZ f ( x, y ) dA . Remember, θ is measured from the x -axis and r is the ray out from the origin through the region. Δ A i 6 = Δ r i Δ θ i Area of a sector of a circle is A = 1 2 r 2 θ . So, Δ A i = 1
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Conversion of a Cartesian Integral to Polar Form where α θ β and a r b Note a and b may be functions of θ , not just numbers. Example 1 Let R be the given region. Write an integral of f ( x, y ) over R in polar form. Example 2 Same as Example 1, but new region shown below. Use polar on circular regions. Use cartesian on rectangular regions. 2
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Example 3 Evaluate
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This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Lecture 13-4 - 13.4 - Double Integrals in Polar Form Recall...

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