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: 11 22 00 x yx yd x d y  18. Calculate the double integral:  ,[ 0 , 1 ] [ 0 , 1 ] ( , ) : 01 , 1 R x dA R x y x y xy  Section 12.3 : 8. Evaluate the double integral: 3 4 ,{ ( , ) | 1 2 , 02 } 2 D y dA D x y x y x x  22. Find the volume of the solid bounded by the planes zx , yx , 2 xy , and 0 z . 24. Find the volume of the solid bounded by the cylinder 4 yz 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 222 x yr and y zr . In problems 40 and 42, evaluate the integral by reversing the order of integration. [Sketch the domain first!!] 40. 3 0 1 y x dx dy 42. 2 33 0 sin( ) x x yd y d x Section 12.4 : 12. Evaluate the given integral by changing to polar coordinates: 4 R x A  , where   (, ) | 4 , 0 Rx y x y x  . In problems 18 and 20, use polar coordinates to find the volume of the given solid. 18. Inside the sphere 16 xyz  and outside the cylinder 4 . 20. Bounded by the paraboloid 12 2 y and the plane 7 z in the first quadrant. 22. (a) A cylindrical drill with radius r 1 is used to bore a hole through the center of a sphere with radius r 2 . Find the volume of the ring-shaped solid that remains.
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This note was uploaded on 02/10/2011 for the course MATH E-21a taught by Professor - during the Fall '09 term at Harvard.

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

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