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EVNREV06 - Review Exercises for Chapter 6 26 From Exercise...

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Review Exercises for Chapter 6 26. From Exercise 21: F 64 15 1 2 2 753.98 lb 28. Solving for x , you obtain x 2 4 1 5 3 2 1 1 1 3 2 y 2 124.8 3 0 3 y y 5 y dy 546.265 lb F 62.4 2 3 0 3 y 4 y 5 y dy L y 2 4 y 5 y x 4 y 5 y . y 5 x 2 x 2 4 h y 3 y 30. x 6 4 2 2 4 6 10 8 6 y 62.4 7 4 0 12 y 16 y 2 dy 21373.7 lb F 62.4 4 0 12 y 7 16 y 2 dy L y 2 7 16 y 2 2 7 16 y 2 h y 12 y 32. Fluid pressure is the force per unit of area exerted by a fluid over the surface of a body. 34. The left window experiences the greater fluid force because its centroid is lower. Review Exercises for Chapter 6 299 2. x 1 2 3 4 1 2 3 5 6 6 (5, 4) 5, 1 25 ( ) 1 2 , 4 ) ( y 4 x 1 x 5 1 2 81 5 A 5 1 2 4 1 x 2 dx 4. ( 1, 1) x 1 2 1 2 3 2 3 2 1 2 y y 1 3 3 1 0 1 3 1 0 y 1 2 dy 1 0 y 2 2 y 1 dy A 1 0 y 2 2 y 1 dy
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300 Chapter 6 Applications of Integration 6. x 1 2 1 2 3 2 3 4 5 (2, 1) (5, 2) y 2 y 1 2 y 2 1 3 y 3 2 1 9 2 2 1 2 y y 2 dy A 2 1 y 3 y 2 1 dy 8. 3 1 x π 2 π 3 π 6 2 π 3 5 π 6 π 6 , 2 ( ) 5 π 6 , 2 ( ) y 2 2 3 ln 2 3 1.555 2 0 3 ln 2 3 2 2 x ln csc x cot x 2 6 A 2 2 6 2 csc x dx 10. x 2 1 2 2 3 1 2 1 2 1 2 3 5 π 3 7 π π 3 , , , ( ( ( ) ) ) y 3 2 3 y 2 sin y 5 3 3 sin y y 2 7 3 5 3 A 5 3 3 1 2 cos y dy 7 3 5 3 cos y 1 2 dy 12. Point of intersection is given by: (.7832, .4804) 1 3 2 4 1.189 3 x 2 x 2 1 3 x 3 1 4 x 4 0.783 0 A 0.783 0 3 4 x x 2 x 3 dx x 3 x 2 4 x 3 0 x 0.783. 14. ( 2, 8) (0, 0) (2, 8) 4 4 2 10 2 4 3 x 3 1 5 x 5 2 0 128 15 8.5333 2 2 0 4 x 2 x 4 dx A 2 2 0 2 x 2 x 4 2 x 2 dx 16. x 2 2 3 4 5 1 1 2 3 (1, 0) (5, 2) y 2 3 x 1 3 2 1 4 x 1 2 5 1 4 3 5 1 x 1 x 1 2 dx A 2 0 2 y 1 y 2 1 dy y x 1 2 x 2 y 1 y x 1 x y 2 1
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Review Exercises for Chapter 6 301 18.
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