test-4-ma242-fall_2017-SOLUTIONS.pdf - MA 242 Fall 2017 Test#4 SOLUTIONS LK Norris 1(15 pts Set-up the triple iterated integral in spherical coordinates

test-4-ma242-fall_2017-SOLUTIONS.pdf - MA 242 Fall 2017...

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MA 242 Fall, 2017 Test #4 - SOLUTIONS LK Norris 1. (15 pts)Set-up the triple iterated integral insphericalcoordinatesthat gives thevalue of the triple integral of the functionf(x, y, z) = (x2+y2+z2)3/2over the regionin the first octant bounded by the spherex2+y2+z2= 9, the half-planesθ=π4andθ=π3, and the planez= 0.DO NOT EVALUATE. 2. (10 pts)One of the following two vector fields is conservative, the other is not. De-termine which one is conservative andthen find all potential functionsfor thatconservative vector field.~F= (2yz)ˆi+ (xz)ˆj+ (xy-3z)ˆk~G= (yz)ˆi+ (xz)ˆj+ (xy+ 2z)ˆk

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