Problem Set 9 Solution

In retrospect we could have decide very early on that

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Unformatted text preview: � 8xyz dx dy dz = W 8xyz dz dy dx �� � 3 �� 9 �� 9−y =8 x y z dz dy dx −3 x2 0 � 3 �� 9 � 2 �9−y � z =8 x y dy dx 20 −3 x2 � � 3 �� 9 y (9 − y )2 =8 x dy dx 2 −3 x2 � � 3 �� 9 2 3 =4 x 81y − 18y + y dy dx −3 −3 3 x2 0 x2 �9 81y 2 y4 3 =4 x − 6y + dx 2 4 x2 −3 � � 3� 8 3 38 81x3 x9 7 −2·3 + =4 x− + 6x7 − dx 2 4 2 4 −3 = 0, � � 3 �2 0 as x, x3 , x7 and x9 are all odd functions. In retrospect, we could have decide very early on that the integral is zero; 9 � J (x) = 9−y �� y � z dz dy, x2 0 is clearly an even function of x, so that...
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