Problem Set 9 Solution

35 2 4 8 y3 y dx 0 12 dy 0 y3 y

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Unformatted text preview: = 0, y = 0 and y 2 = 4 − x. So, reversing the order of integration, we get � 4 �� √ � 4−x x dy 0 � 4 dx = 0 √ x [y ]0 4−x dx 0 � = 4 √ x 4 − x dx 0 � �4 � 4 2x 2 3/2 + (4 − x)3/2 dx = − (4 − x) 3 03 0 � �4 4 =− (4 − x)5/2 3·5 0 7 2 = . 3·5 2 4. � 8 �� √ � y/3 y dx 0 � 12 �� √ dy + 0 � y/3 √ y −8 8 y dx 2 � �� � x2 +8 dy = y dy 2 � = 0 2 � dx 3x2 0 = 0 � y2 2 �x2 +8 dx 3x2 (x2 + 8)2 (3x2 )2 − dx 2 2 8x3 9x5 x5 + + 25 x − = 2·5 3 2·5 9 · 24 24 26 + + 26 − = 5 3 5 896 = . 15 � 5. 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 y = x2 and y = 9. ��� � 3 �� 9 9−y �� ...
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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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