Question

please don't write in Cursive as i cant read it. And please write it in a clear handwritting. NO CURSIVE please

4. (a) Find the centroid of the region bounded by y = x + y = x', and x = (b) Find the centroid of the region bounded by (x - 2)2 + (y + 3)2 = 25. (10 points) (5 points)

Answer 1

Given Cuares, y=플러를 ,y-2 , x= 4 from graph, x lies from 소 4 toI Arco - I (PR) - ( lange) A- / (꽃+)-(x) dx - 4 2(2) T + ], 2. 4 A 여를 4 + 生 (4) + (402 (44) 1 A 4. G4 + 1 1024 8 쁘 A= 512 - 16 + 128-1 1024 623 1024 NON, Mx ) a (() (+)- (x² 이이이 4. My= 소 2 da 4 + 1 3 Ma 12 전 7 2 4(3) 2(2) 1. 4 1 4 (12(4) 4(4) 4(4) (), Mai - 2. 1 768 4 16. | 64 111688 [ - 을 Mx 2. 28672 + [72032 - 4112 - 2014 G - 1376 -3 344064

Mn = 2/3 144125 344064 = 144125 688128 6 Then, My S*((4+4)(?)) dx May ( 13 14-234 My = (in X х 2(3) 2(2) 1 5 21/9 1 6(43 4(4) (435 My = 1 2560+ 3840 - 3072 – 40 – 240+ 3 3051 15360 15360 :. Coordinates of Centre of mass centroid are Ža My 3051 A 15360 3051 0.3265 15(623) 1024 623 Mr А. 144125 688126 623 1024 144125 (672)623 0.3443 as centroid (8,9) = (0-32 6S, Q. 314 3) e Given (x-2)+(4+3)=25 is of form (x-h) + (y-K)=ye which is crete equation with Centre Chok) and radius j'. Here centre (hik) = (2,-3). for, Circle Centre is the centroid. .: (2,5) = (2,-3).

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