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Unformatted text preview: a) (10) Compute dxdy in terms of dudV if u = x 2 /y and V = xy . b) (10) Find a double integral for the area of R in uV coordinates and evaluate it. 6. a) (5) Let C be a simple closed curve going counterclockwise around a region R . Let M = M ( x, y ). Express c C Mdx as a double integral over R . b) (5) Find M so that c C Mdx is the mass of R with density δ ( x, y ) = ( x + y ) 2 . 7. Consider the region R enclosed by the x-axis, x = 1 and y = x 3 . a) (5) Use the normal form of Green’s theorem to ±nd the ²ux of v F = (1 + y 2 )ˆ out of R . b) (5) Find the ²ux out of R through the two sides C 1 (the horizontal segment) and C 2 (the vertical segment). c) (5) Use parts (a) and (b) to ±nd the ²ux out of the third side C 3 ....
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This note was uploaded on 04/18/2008 for the course 18 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08