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Integ_tut_sol2 - Integration II Solutions for Integration...

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Integration II Solutions for Integration II Exercises 1. ( 29 2 y 4x x x 4 x when x 2, y 4 = - = - = = ( 29 ( 29 1 2 4 6 2 2 0 4 4 6 3 3 2 2 0 4 Area A A 4x x dx 4x x dx x x 2x 2x 3 3 64 216 64 32 72 32 3 3 3 32 32 64 3 3 3 = + = - - - = - - - = - - - - + = + = 2. ( 29 2 2 2 2 y 16x y 4 x When y 16x and y 3x meet 16x 9x 16x 9x 0 x 16 9x 0 16 x 0 or x 9 = = ± = = = - = - = = = ( 29 16 9 1 2 0 16 9 3 2 2 0 Area 4x 3x dx 8 3 x x 3 2 8 64 3 256 3 27 2 81 256 128 162 81 = - = - = - = = 1 0 1 2 3 4 5 6 7 0 1 2 3 16/9 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 -4 -2 0 2 4 6 8 A 2 A 1
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Integration II 3. 7 8 7 8 8 7 8 1 8 7 8 7 8 1 8 7 8 1 8 7 8 7 63 8 63 8 a y x and a x y x y and y a x a Curves meet when x a x a x a x a x a - + = = = = = = = = ( 29 a 7 8 1 8 7 8 0 a 7 8 9 8 7 9 0 7 8 9 8 7 9 2 2 2 Area a x a x dx 8 1 a x a x 9 9 8 1 a a a a 9 9 8 1 7 a a a 9 9 9 - - - = - = - = - = - = 4. 18 1 2 0 18 3 2 0 Area 2 2 x dx 2 2 2 x 3 4 2 54 2 144 3 = = = = ( 29 y 18 3 2 y 0 18 5 2 0 5 5 M xy x M 2 2 x dx 2 2 2 x 5 4 2 3 2 5 32 3 1555.2 5 1555.2 x 10.8 144 δ = δ = =
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