randolph3

# Randolph3 - Z 1 Z 1 √ x Z 1-y dz dy dx using the order dxdz dy(Don’t evaluate 6[24pt SET UP(don’t evaluate integrals whose values give(a The

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Math 22 Exam #3 Name Fall 2000 1. [10pt] Calculate the value of the iterated integral Z 3 0 Z 9 y 2 y cos( x 2 ) dxdy . 2. [10pt] Calculate the volume of the region inside the cylinder x 2 + y 2 = 4, above the xy -plane and under the graph of z = e - ( x 2 + y 2 ) . 3. [16pt] (a) SET UP an iterated integral whose value gives the area of the region in the ﬁrst quadrant that lies inside the circle x 2 + y 2 = 2 y and outside the circle x 2 + y 2 = 1. (b) Calculate ZZ D dA , where D is the region in part (a). 4. [15pt] This question concerns a lamina that occupies the region bounded by graphs of the equations y = x and x + y = 2, and has density that is proportional to the distance from the origin. (a) SET UP (don’t evaluate) an iterated integral with limits whose value is the mass. (b) SET UP (don’t evaluate) an integral which gives the ﬁrst moment about the x -axis. 5. [10pt] Rewrite the integral
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Unformatted text preview: Z 1 Z 1 √ x Z 1-y dz dy dx using the order dxdz dy . (Don’t evaluate). 6. [24pt] SET UP (don’t evaluate) integrals whose values give: (a) The surface area of the part of the sphere x 2 + y 2 + z 2 = 4 that lies above the plane z = 1. (b) The volume of the region bounded above by the sphere x 2 + y 2 + z 2 = 4 and below by the plane z = 1, i. using cylindrical coordinates. ii. using spherical coordinates. 7. [15pt] Consider Z 2 Z √ 4-x 2 Z 2 √ x 2 + y 2 dz dy dx (a) Convert the given integral to an equivalent interated triple integral in terms of cylindrical coordinates. Don’t evaluate . (b) Convert the given integral to an equivalent interated triple integral in terms of spherical coordinates. Don’t evaluate ....
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## This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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