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Unformatted text preview: r on the portion of the curve y = x 2 from (0 , 0) to (1 , 1). 5. Consider the region R in the ±rst quadrant bounded by the curves y = x 2 , y = x 2 / 5, xy = 2, and xy = 4. 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 Mdx as a double integral over R . C b) (5) Find M so that Mdx is the mass of R with density δ ( x, y ) = ( x + y ) 2 . C 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 ﬂux of F v = (1 + y 2 )ˆ out of R . b) (5) Find the ﬂux 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 ﬂux out of the third side C 3 ....
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This note was uploaded on 05/04/2011 for the course MATH 18.02 taught by Professor Auroux during the Spring '08 term at MIT.
- Spring '08
- Multivariable Calculus