Triple integral - solid tetradhedon

[Whatupdoc]

Evaluate the triple integral \int \int \int xy*DV where E is the solid
tetrahedon with vertices (0,0,0), (4,0,0),(0,1,0),(0,0,7)

first I'm going to find n:
AB= <-4,1,0>
AC= <-4,0,7>
AB X AC = <7,28,4> = n

so i get this equation: 7(x-4) + 28y + 4z = 0
=> 7x+28y+4z = 28

so the bounds of z should be z = 0..28-7x-28y

solving for y gives me the bounds for y = 0.. 1-1/4*x

and the x bounds x = 0..1

are my bounds correct?

 

[hypermorphism]

...
=> 7x+28y+4z = 28
so the bounds of z should be z = 0..28-7x-28y
...

Don't forget that z had a coefficient of 4.