Thread: Help with setting up bonds in a triple integral

Hi,

Here is the problem i am working on...
evaluate the triple integral ∫∫∫ xy dV where E is the solid tetrahedron with vertices (0,0,0), (6,0,0), (0,1,0) and (0,0,7).

I sketched the region and got the following limits..
for x--- x=0 to x=6(1-y)
for y- - - y=0 to y=1
for z----z= 0 to z= 7(1-x/6-y)

i evaluated the integral with the order of integration dzdxdy and i got 15 but it's wrong.

can someone explain me if my bouds or order of integtation are wrong,
thank you

Originally Posted by Candy21

Hi,

Here is the problem i am working on...
evaluate the triple integral ∫∫∫ xy dV where E is the solid tetrahedron with vertices (0,0,0), (6,0,0), (0,1,0) and (0,0,7).

I sketched the region and got the following limits..
for x--- x=0 to x=6(1-y)
for y- - - y=0 to y=1
for z----z= 0 to z= 7(1-x/6-y)

i evaluated the integral with the order of integration dzdxdy (Everything is correct up to here!) and i got 15 but it's wrong.

can someone explain me if my bounds or order of integration are wrong,
thank you

The integral is . After doing the x-integral, I get .