Question

calc 3 Question - Help
http://tutorial.math.lamar.edu/Classes/CalcIII/TripleIntegrals.aspx on Example 2 in this site, for 2x+3y+z=6, I don't understand how he made that triangle, the region D in the xy-plane. How did he manage to find those vertices/coordinates??

Answer 1

@Hoa dude, ur comments got deleted for some reason. Can you please explain again?

Answer 2

I understand the problem in very very simple way, you have 8 ways to construct the form, right?

Answer 3

to calculate an integrate, you just need 2 planes to construct the form.

Answer 4

got it, friend?

Answer 5

to find the upper and lower bounds of a variable like x, you make the other variables equal to 0?

Answer 6

ask for other's opinion, I am not confident to express my mind in the front of others whose smartscore too high like the guy watching us

Answer 7

lol hoa XD

Answer 8

I don't make up. It's originally there. of course, to xy plane, z =0

Answer 9

It's a smiley face. The eyes are closed, forming an X shape. The D is a big open mouth.

Answer 10

@zepdrix answer him, help us, I want to learn, too.

Answer 11

Ok, gimme a few minutes c: thinking.

Answer 12

So yah the region is a little trickier to understand in 3 dimensions I guess.
To find the `trace` in the xy-plane, we simply let z=0.

\[\large 2x+3y=6 \qquad \rightarrow \qquad y=-\frac{2}{3}x+2\]

Answer 13

So if we graph this, it looks something like this I guess.