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Mathematics
OpenStudy (anonymous):

need help re-expressing the bounds of a triple integral. Q: consider the solid in the first octant bounded by the planes y=x, z=y and z=4 write the integral as an iterated triple integral with order of integration dxdydz, dzdxdy, and dydxdz

OpenStudy (anonymous):

Can you include the picture? I've seen it before but it helps xP

OpenStudy (anonymous):

yeah sure can hold on

OpenStudy (anonymous):

OpenStudy (anonymous):

Well, for dxdydz. x is going to range from 0 to y. Then y is gonna range from z to 4. Then z is gonna range from 0 to 4. Does that make sense? (If I'm seeing this right)

OpenStudy (anonymous):

dxdydz :i got x: from 0 to y y: from 0 to z z: from 0 to 4

OpenStudy (anonymous):

But that would give you the wrong region, look at the colored region, y doesn't start at zero always, it ranges. :/

OpenStudy (anonymous):

As z because you have y=z

OpenStudy (anonymous):

okay that makes sense now that im looking at the picture but how would it change if you were to do dzdxdy ?

OpenStudy (anonymous):

y would range from 0 to 4 i think but what about the rest?

OpenStudy (anonymous):

Okay. Well z would range from y to 4. Then x would range from from 0 to y then y would be 0 to 4.

OpenStudy (anonymous):

Because you have z=y then the max is 4. X goes from x=y, it goes from zero since its bounded by y=0. Then y goes from zero to 4.

OpenStudy (anonymous):

The easiest thing to do, is once you get the first bounds, let it go to zero then look at the "shadow" this will give you a triangle (for this problem) from there, it is easier (per se).

OpenStudy (anonymous):

ohhhhh okay that helped alot. so for the last one dydxdz z will go from 0 to 4, x will be from 0 to y and y will go from z to 4?

OpenStudy (anonymous):

As far as I can tell :)

OpenStudy (anonymous):

sweet! thanks for the help this makes so much more sense now

OpenStudy (anonymous):

You're welcome :) Any other questions just post them in the feed xP

OpenStudy (anonymous):

thanks will do! :)

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