Calculus Solutions 27

Calculus Solutions 27 - A-26 Answers to Odd-Numbered...

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Unformatted text preview: A-26 Answers to Odd-Numbered Problems &L .-L 37 + q L ! = , C L f (n, ~ ) i s e x a c t f o r f = 1 , x , y , x y 39Volume8.5 41Volumesln2,2ln(l+&) n &dy $ : = xydx dy J : $ : 4 3 45 W i t h long rectangles 1 1 Ins = ln2;J0 lo xydy dx = $' o " - l d x = In2 y i A A = A A = 1 but $$ y d A = Section 14.2 Change to Better Coordinates (page 534) Wdu dv 1 $:;i4 $ : 1 dl-"' 5 R is symmetric across the y axis; So So u du dv = 5 divided b y area gives (a, U ) = ( 4 / 3 r , 4 / 3 4 '+-dy dx; xy region R* becomes R in the x*y* plane; dx dy = dx'dy* when region moves 7 2So I * Sl+x g J = COSO* -r*sinO* = r*; $:7i4 so1 r*dr*dO* 1 1 Iy = $$Rx2dx dy = $:Y/~$: r2cos2O r dr do = 5 - i; Is = 5 + i; I. = 13 (0,0), (1,2), (1,3), ( 0 , l ) ; area o f parallelogram is 1 15 x = u , y = u + 3v + uv; then ( u , v ) = (1,0), (1, I ) , ( 0 , l ) give corners ( x , y) = (1,O ) , (1,5), (0,3) 3 17 Corners (0,0), (2,1), (3,3), (1,2); sides y = i x , y = 22 - 3, y = i x + 5 ,y = 22 I 9 Corners (1, I ) , (e2, e ) , (e3, e 3 ) ,...
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