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Unformatted text preview: Theorem. Fubini’s Theorem If f ( x, y ) is continuous on the rectangular region R : a ≤ x ≤ b , c ≤ y ≤ d , then Notes about the double integral of f ( x, y ) over a rectangle R 1. 2. Think of a double integral as the integral of an integral. Calculate from the inside out. Example 1 Z 6 Z 3 1 2 x + 3 y + 5 dydx 3 Example 2 Z 3 1 Z 6 2 x + 3 y + 5 dxdy Do. Z 21 Z 3 1 xy 2 dydx 4 Example 3 ZZ R xye xy 2 dA , R : 0 ≤ x ≤ 2, 0 ≤ y ≤ 1 Example 4 Find the volume of the solid bounded by the elliptic paraboloid z = 1+( x1) 2 +4 y 2 , the planes x = 3 and y = 2 and the coordinate planes. 5...
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 Spring '03
 MECothren
 Integrals, Multivariable Calculus, Angles, Defn. Deﬁnite Integral, Deﬁnite Double Integral, little rectangle Vk

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