You need to perform the following substitution, such that `36 - x^2 = t => -2xdx = dt => xdx = -(dt)/2`
Replacing the variable yields:
`int_0^3 (xdx)/(sqrt(36 - x^2)) = -int_(t_1)^(t_2) (dt)/(2sqrt t) = -sqrt t|_(t_1)^(t_2)`
Replacing back the variable yields:
`int_0^3 (xdx)/(sqrt(36 - x^2)) = -sqrt(36-x^2)|_0^3`
`int_0^3 (xdx)/(sqrt(36 - x^2)) = -sqrt(36 - 9) + sqrt(36-0)`
`int_0^3 (xdx)/(sqrt(36 - x^2)) = 6 - sqrt 27`
`int_0^3 (xdx)/(sqrt(36 - x^2)) = 6 - 3sqrt 3`
`int_0^3 (xdx)/(sqrt(36 - x^2)) = 3(2 - sqrt3)`
Hence, evaluating the definite integral, yields `int_0^3 (xdx)/(sqrt(36- x^2)) = 3(2 - sqrt3).`
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