Set 12 Solutions.pdf - ESE 318-02 Fall 2018 Homework Set#12...

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ESE 318-02, Fall 2018 Homework Set #12 Due Tuesday, Nov. 27 1 . Zill 9.10.15. 2 . Zill 9.10.18. 3 . Zill 9.10.26. 4 . Zill 9.10.28. 5 . Zill 9.10.30. Use rectangular coordinates. 6. Zill 9.10.30. Use polar coordinates. 7 . Zill 9.10.34. 8 . Zill 9.11.8. 9 . Zill 9.11.25. 10 . Zill 9.11.28. 11 . Zill 9.11.31. 12 . Zill 9.11.32. (Hint: variable substitution.) Solutions 1 . Zill 9.10.15 Area is between y = x 2 and y = x 3 , for 0 < x < 1. 84 25 7 4 3 24 28 21 7 2 3 1 4 1 1 0 7 7 2 3 3 1 4 4 1 1 0 6 2 3 1 0 3 6 4 2 4 3 1 0 2 1 0 3 2 2 2 2 2 2 2 2 1 4 2 1 4 2 , 1 4 2 2 3 2 3     x x x dx x x x dx x x x x x x dx y y xy dx dy y x dA y x x y x y dA y x x x y x x R R
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ESE 318-02, Fall 2018 2 . Zill 9.10.18. The curves meet at x = 1 and -1. 2 2 3 , 1 x y x y dA y x R          0 2 2 2 2 1 3 2 1 2 3 1 2 3 2 2 3 , 1 2 / 3 2 / 3 3 2 2 / 3 2 / 3 3 2 1 1 2 / 3 2 3 2 1 1 2 / 3 2 3 2 1 1 2 1 1 2 / 1 2 1 1 2 / 1 2 2 / 1 2 1 1 3 1 2 / 1 1 1 3 1 2 / 1 2 2 2 2 2 2    x x xdx x dx x x dx x x x x dx xy dx dy xy x y x y dA y x du u du u x x y x x R   3 . Zill 9.10.26. 0 , 0 , 0 , 3 4 2  z y x x dA y R Since one boundary is z = 0, a boundary on y is 2. So the region of integration is a rectangle. Also, the integral can be broken down as a product.
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