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by: Zechariah Hilpert
Zechariah Hilpert
GPA 3.8


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Class Notes
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This 1 page Class Notes was uploaded by Zechariah Hilpert on Thursday September 17, 2015. The Class Notes belongs to MATH 234 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 50 views. For similar materials see /class/205288/math-234-university-of-wisconsin-madison in Mathematics (M) at University of Wisconsin - Madison.

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Date Created: 09/17/15
H 3 9 7 Cf 03 5 00 3 Math 234 Worksheet 4 Sketch the region of integration and calculate the integral 1 1722 0 2 y zzdzdydm 71 0 ix 17m27y2 Find the volume of the region that is above the cone b 7r3 and inside the sphere p 1 Answer 7r3 A homogeneous solid is the intersection of the cone 2 2 2 1122 and the ball z y 22 S 5 a Find the volume V of the solid b Find the z coordinate 2 of the center of mass of the solid The sold Sis cut out from the ball zzy222 S 1 by the half cone z 22 yz Find the volume of S Find the volume of the solid bounded by the paraboloid z 2 y2 and that is inside the cylinder 2 y2 9 and above the plane 2 0 Evaluate the line integral fc1 7 xds7 where C is a portion of the cirle of radius 2 and center 07 07 traversed from 20 to 02 Hint The curve can be parametrized as x 2cos t y 2sint7 0 S t S Answer 7139 7 4 Calculate fC3x y2dz cosey 1dy7 where C is the boundary of the triangle with vertices 17 71 07 0 and 027 oriented clockwise A homogeneous wire 0 in the xy plane is the part of the circle 22 y2 9 in the rst quadrant z 2 07 y 2 0 Find the center of mass 713 of the wire Compute fffRzz 2zdV7 where R is the region in the rst octant bounded by 2 22 4 and z y 2 Answer Find the maximum volume of the closed rectangular box with faces parallel to the coordinate planes inscribed in the ellipsoid 2 2 2 y 2 z 7 7 3 4 9 Set up the triple integral of fxyz over the tetrahedron with vertices 07 007 2107 057 0 and 003 as a repeated integral in the order dzdydx A container V is lled with a liquid mixture that has density proportional to the depth of the liquid according to the formula 627y72 02 where c is a xed constant The container V is de ned to be the volume of the region bounded by the surfaces 2 4 2x2 2 127 y 22 and y 0 Find the mass of the liquid in V


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