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QUESTION: Calculate 3.xy’dA, where D is the region bounded by the points (0,0), (3,1), (0,3). ce Integrate over region bound by (0,0), (3,1), (0,3). Region is a traingle, defined as follows: D = {(x, y) 0<x<3, 2/3 Sy = –22/3+3} 3 3–20/3 2 0 2/3 [/ seran = T *31* dsly = 3 ) = 5 * * * - 6x +9] ex - 3 /* * dx +45* xdx-91*** dx + 21 "x dx = + 2*1* – 38°* + 27% JO Jo 75 33 27x23 323/ + 15 lo 10 lo 2 lo

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Answer 1

tounded in 10,0), (3,1),(0,31 yg (0,34 h . 307 Glearly y is going from 4 to L2 je y=2 to Y= 2-24 and lly x is going from Zero Lone equations s3-2013 -4 = 4 = x/3 = 4-3=(x-0 (1-37 (3-0 J = 2x +3 dA=dady limits kd n (0,3) 30 Tbc I: 3fx [27 1 2 3 27 T: 36 x | 21-843 - 182, +424 '] de 27-803 - 1 2 x3 1 da 27 27

1:37 (97 - 18 [21] +[81] - 27x9 15 243 10 Just we have to drive the line equation 2 Then We have to part kimits from whese & and y are going ic gey to y = y ₂ (n=u, to u=x2) Tag - 247 [03] T3 3 then we have to Integrate Integral pust Wat y treating kconst then ast w treatine y const After Integriting but the values, 4

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Issue with given answer in question:-

Integration done in above method is ambiguous or incorrect not according to the rules of integration.