The area (in square units) bounded by the curves y = $straight y space equals space square root of straight x comma$ 2y-x+3 =0, X -axis and lying in the first quadrant is

9

36

18

27/4

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Solution

2 space square root of straight x space equals space straight x minus 3 4 straight x space equals space straight x squared minus 6 straight x space plus space 9 straight x squared minus 10 straight x plus 9 straight x space equals 9 comma space straight x space equals 1 integral subscript 0 superscript 3 left parenthesis 2 straight y space plus 3 right parenthesis minus straight y squared right square bracket dy open square brackets straight y squared plus 3 straight y minus straight y cubed over 3 close square brackets subscript 0 superscript 3 space equals space 9 plus 9 minus 9 space equals 9

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