Problem Set 9 Solution

8 7 this is the region bounded by the planes y 1 x

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Unformatted text preview: xJ (x) is an odd function. 6. This is a region of type 4; we view this as an elementary region of type 1. The projection of W onto the xy -plane is the elementary region of type 2 bounded by x = 0, y = 3 and y = x. ��� � 3 �� 3 �� √ z dx dy dz = W � 9−y 2 z dz 0 � x 3 = ⎛ 0 3 � ⎝ 0 x 3 3 � 2 z 2 �√9−y2 �� 4 dy dx ⎞ dy ⎠ dx 0 � 9 − y2 = dy dx 2 0 x �3 �� 13 y3 = 9y − dx 20 3x � 13 x3 = 18 − 9x + dx 20 3 � �3 1 9x2 x4 = 18x − + 2 2 12 0 4 3 3 3 = 33 − + 4 8 3 3 = (8 − 6 + 1) 8 81 =. 8 � � 7. This is the region bounded...
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This note was uploaded on 11/23/2013 for the course MATH 18.022 taught by Professor Hartleyrogers during the Fall '06 term at MIT.

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