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paraboloid

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**Volume of Tetrahedron[Solved]**

My text book opts to integrate with respect to y before x(dydx vs dxdy), so I assumed that it would not affect the outcome.

I set the upper and lower bounds of y, respectively, as y = 24 - 7x/4 (from 7x+4y=96) to y = x/4 (from x = 4y). For x I set it from upper bound x = 12 (using x/4 = 24 - 7x/4) to lower bound x = 0 (given).

Integrating with respect to y, I get [tex]\int(96y - 7xy - 2y^2)|dx[/tex] which after inputing the bounds become [tex]\int(1152-144x+8x^2)dx[/tex]. After integrating this I get [tex](1152x - 72x^2 + 8x^3/3)|[/tex].

Computing this I get 1152(12) - 72(144) + 8(1728)/3 = 13824-10368+4608 = 8064.

I've been at this for a few hours now, but I can't seem to find my error.

Any help would be great,

Thanks in advance

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