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Unformatted text preview: (1 , 0) of radius a n = 1. Consider the cases a > 1 and a < 1 separately. Explain your answers with diagrams. Optional: use the applet on the course web page to get a better understanding of what happens when a changes from a value lower than 1 to a value greater than 1. Problem 2. (Thursday, 4 points) Do 14.6/39. (Suggestion: use the order dxdy dz . The numerical answer is in the back of the text. Feel free to check your work using it.) Problem 3. (Friday, 4 points) The average value of f ( x,y,z ) over a region D in space is 1 V ( D ) iii D f ( x,y,z ) dV, V ( D ) = volume of D Set up the integral both in cylindrical and spherical coordinates for the average distance from a point in the solid sphere of radius a to a point on the surface, and evaluate both integrals. Put the point on the surface at the origin and make it the South Pole of the sphere. Problem 4. (Friday, 4 points) Notes 5C/5....
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This note was uploaded on 04/28/2009 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
 Fall '08
 Auroux
 Integrals

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