Lecture12 - Lecture 11 Double integrals Lecture 11 Double integrals Objectives 1 Interpret integrals as volumes 2 Define average value of a

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Unformatted text preview: Lecture 11: Double integrals May 28, 2009 Lecture 11: Double integrals Objectives 1 Interpret integrals as volumes. 2 Define average value of a function. 3 Use partial integration to evaluate double integrals on rectangles. 4 Use partial integration to evaluate double integrals on more general regions. Lecture 11: Double integrals Integration in one dimension. Z b a f ( x ) dx = lim N →∞ N X i =1 f ( x * i )Δ x ! When f ( x ) > 0, the integral is interpreted as the area between the graph of f ( x ) and the x-axis between the points a and b . Lecture 11: Double integrals Integration in two dimensions ZZ R f ( x , y ) dA = lim m , n →∞ n X i =1 m X j =1 f ( x * ij , y * ij )Δ A R = { ( x , y ) | a ≤ x ≤ b , c ≤ y ≤ d } When f ( x , y ) > 0, the integral is interpreted as the volume between the graph of f ( x , y ) and the xy-plane, bounded by the rectangle R . Lecture 11: Double integrals Class exercise ZZ R (5- x ) dA R = { ( x , y ) | ≤ x ≤ 5 , ≤ y ≤ 3 } Lecture 11: Double integrals Class exercise ZZ R (5- x ) dA R = { ( x , y ) | ≤ x ≤ 5 , ≤ y ≤ 3 } Answer: 75 2 Lecture 11: Double integrals Properties of double integrals...
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This note was uploaded on 04/29/2010 for the course MATH 200 taught by Professor Unknown during the Spring '03 term at The University of British Columbia.

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Lecture12 - Lecture 11 Double integrals Lecture 11 Double integrals Objectives 1 Interpret integrals as volumes 2 Define average value of a

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