Final Unknown

Final Unknown - MATH 52 FINAL EXAM 1(a Sketch the region R...

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Unformatted text preview: MATH 52 FINAL EXAM 1. (a) Sketch the region R of integration in the following double integral. integraldisplay 1 integraldisplay 1 √ x xe y 5 dy dx (b) Express the region R as an x-simple region. (c) Evaluate the integral by changing the order of integration. 2. (a) Let T be a solid cone whose base is the disk x 2 + y 2 ≤ 1 in the xy-plane and whose vertex is the point (0 , , 2). Set up, but do not evaluate, a triple integral in cylindrical coordinates which computes the moment of inertia of T around the x-axis. (b) Let T be the solid ball of radius 1 centered at (2 , , 0). Set up, but do not evaluate, a triple integral in spherical coordinates which computes the moment of inertia of T around the z-axis. Hint: First consider the change of variables u = x- 2, v = y , w = z . 3. Consider the curve C parametrized by r ( t ) = (2 e t , 1 3 e 3 t + e- t ) for 0 ≤ t ≤ 1. (a) Find the arclength of C ....
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This note was uploaded on 04/16/2008 for the course MATH 52 taught by Professor Demanet,l;wieczorek,w during the Winter '08 term at Stanford.

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Final Unknown - MATH 52 FINAL EXAM 1(a Sketch the region R...

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