HW 9 - Math E-21a Fall 2009 HW#9 problems Problems to turn...

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1 Math E-21a – Fall 2009 – HW #9 problems Problems to turn in on Thurs, Nov 5 : Section 12.2 : 12. Calculate the iterated integral: 1 1 2 2 0 0 xy x y dx dy   18. Calculate the double integral: , [0,1] [0,1] ( , ) :0 1,0 1 1 R x dA R x y x y xy  Section 12.3 : 8. Evaluate the double integral: 3 4 , {( , ) |1 2,0 2 } 2 D y dA D x y x y x x  22. Find the volume of the solid bounded by the planes z x , y x , 2 x y , and 0 z . 24. Find the volume of the solid bounded by the cylinder 2 2 4 y z and the planes 2 x y , 0 x , 0 z in the first octant. 26. Find the volume of the solid bounded by the cylinders 2 2 2 x y r and 2 2 2 y z r . In problems 40 and 42, evaluate the integral by reversing the order of integration. [Sketch the domain first!!] 40. 1 1 3 0 1 y x dxdy   42. 2 1 1 3 3 0 sin( ) x x y dy dx   Section 12.4 : 12. Evaluate the given integral by changing to polar coordinates: 2 2 4 R x y dA  , where 2 2 ( , ) | 4, 0 R x y x y x . In problems 18 and 20, use polar coordinates to find the volume of the given solid. 18. Inside the sphere 2 2 2 16 x y z and outside the cylinder 2 2 4 x y . 20. Bounded by the paraboloid 2 2 1 2 2 z x y and the plane 7 z in the first quadrant.
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