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Unformatted text preview: value of I . Problem 4. (15) Use the divergence theorem to compute the ﬂux of F = i + j + k outwards across the closed surface x 4 + y 4 + z 4 = 1. Problem 5. (15) Consider the surface S given by the equation z = ( x 2 + y 2 + z 2 ) 2 . a) Show that S lies in the upper half space ( z ² 0). b) Write out the equation for the surface in spherical polar coordinates. c) Using the equation obtained in part b), give an iterated integral, with explicit integrand and limits of integration, which gives the volume of the region inside this surface. Do not evaluate the integral. Problem 6. (15) Let S be the part of the surface z = xy where x 2 + y 2 < 1. Compute the ﬂux of F = y i + x j + z k upward across S by reducing the surface integral to a double integral over the disk x 2 + y 2 < 1. 1...
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- Spring '08
- Multivariable Calculus, Stokes' theorem, Practice Exam 4A, MIT OpenCourseWare http://ocw.mit.edu