Multivariable Calculus Double Integration Problem

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methstudent
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1. Find the volume of the region above the triangle in the xy-plane with vertices (0,0) (1,0) (0,1) and below the surface z =f(x,y)=6xy(1-x-y)

My attempt is attached
 
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  • Handwritten double integral work: integral from 0 to 1 and 0 to 1-x of 6xy - 6x^2y - 6xy^2 dy dx, followed by antiderivative steps, expansion, and a final result of 1/200. A small sketch shows a triangle with vertices (0,0), (1,0) and (0,1).
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You might want to check your addition of the fractions at the end of the calculation.
 
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yeah, I accidentally put an extra zero on the 20. thanks!