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Unformatted text preview: of the unit disk in R 2 . Find ex 2 + y 2 ( 29 D âˆ«âˆ« dxdy . 5. Set up, but do not evaluate , an integral to find the surface area of the portion of the sphere x 2 + y 2 + z 2 = 16 between the planes z = 1 and z = 2. 6. Suppose V = dydxdz 4x 2 âˆ« 4x 2 âˆ« 4 âˆ« . Sketch the solid whose volume is given by V . Be sure to label parts of your surface appropriately. 7. A sphere of radius k has volume 4 3 p k 3 . In each of the three coordinate systems, set up a triple integral that represents this volume. Do not evaluate the integrals. 8. Using the transformation u = x + y , v = y2 x , show how the ellipse 5 x 22 xy + 2 y 2 = 1 in the xyplane becomes a circle in the uvplane. Find the area inside the ellipse by using this transformation....
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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.
 Winter '08
 BRIGHAM
 Math

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