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Lecture #26-27. Triple Integrals in rectangular coordinates. CH 15.4

Lecture #26-27. Triple Integrals in rectangular coordinates. CH 15.4

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Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 Definition of Triple Integrals. Function ( 29 , , F x y z is defined on a closed bounded region D in space. Using planes parallel to coordinate planes can be done partition of D into rectangular cells. Elementary k -th cell has dimensions , , k k k x y z . 1
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Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 ( 29 1 , , n n k k k k k S F x y z V = = ( 29 0 lim , , n P D S F x y z dV x = ��� or ( 29 0 lim , , n P D S F x y z dxdydz x = ��� Volume of a Region in Space. If ( 29 , , 1 F x y z = , then D V dV = ��� . 2
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Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 Finding the Limits of Integration. Box-Like Regions. Problem #1. Evaluate ( 29 1 2 2 2 0 1 1 x yz dzdydx + ��� . 3 ( 29 ( 29 , , , , b d s D a c r F x y z dV dz dy F x y z dx = ��� ���
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Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 General Regions Enclosed by Curved Surfaces. Suppose that ( 29 ( 29 1 2 , , f x y z f x y x . To evaluate ( 29 , , D F x y z dV ���
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Unformatted text preview: region D , integrate first with respect to z , then with respect to y , finally with respect to x . 4 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 5 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 1 1 , , , , y g x z f x y x b x a y g x z f x y F x y z dxdy dz = = = = = = 6 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 Other types of Regions. Problem #2. 7 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 Problem #3. Volumes Using Triple Integrals. Problem #4. 8 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 9 Math 234 SS 2008 CH. 15.4. Triple Integral in Rectangular Coordinates. Lectures #26-#27 Properties of Triple Integrals. 10...
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