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Unformatted text preview: (9) ( Hard! ) Does the integral H d A 1 + x + y converge, if H is the half-strip deFned by 0 < x < 1 and y > 0? What if we replace y by y 2 in the integrand? You might like to check (and use!) the inequalities ln ( 1 + t ) t and 1 1 ( 1 + u ) 2 , which are valid for t 0 and u 0, respectively. (10) ( Hard! ) Consider the integral R x 2-y 2 x 2 + y 2 d x d y , where R is the region bounded by the curves y = x , y = x / 3, xy = 1 2 and xy = 2. Evaluate this integral using both (a) polar coordinates, r = x 2 + y 2 and = arctan ( y / x ) , and (b) the coordinates u = xy and v = y / x ....
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This note was uploaded on 10/02/2010 for the course ENGINEERIN MATH 262 taught by Professor Rix during the Fall '10 term at McGill.
- Fall '10