Question

1. (4 points) Evaluate the double integral on the given domain D xy where D={(x,y):25x54,15ys3} 2. (4 points) Evaluate the double integral on the given domain S dxdy © 1(x2 + y2)3 where D=(x,y):15x2 + y2 <4, yzo}

Answer 1

I Given that domain is ! si C D = f (x, y): 2 X 14, 12 y 234 A60B (4,1) - tx The domain D is the Shaded figure o - line ranges of iş à 2 to nag ranges off is pr 1 to ý : double integration is t o ta JS tag dr dy stain tai dy 3 - (11 dk) Usado) si go Double integ- tration separated = { bacon)Le to single integration = (hoge) - 6099) (hoge brytes in iznis I loalt ) ) loggi che llogg23Ilog (3) in Terefore, Storia dla dy = (logie) (hoge)) 40 - D

E 2. Given that the domain Dis . AL X + y 24 , y D Da +994 010 The ..Given Shaded region is the required domain. the double integration Maryoga.com - Changing the Cartesian Co-ordinate system to polar Co-ordinate system'" by the transformation x=rcoso, yor. Sin e. . locail magnitude factor 27 2., coso ersino sino rcoso so, dady=j drdo. for polar Co-ordinate system, the domain is =f(ro) : 1trrosto tr" sino 2a. 040 LM 1 (8,0): 128 24, osotal -{(1,0): 1 ?*32, 0nl iz drudy = J Jericost otrosno 3 Jardo Ø 1**97° polar coordinat Polar co-ordinate domain

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