00:01
Okay, so we have a tetrahedron.
00:06
Tetrahedron is our bread and butter in multi -calculus really.
00:13
Almost every question is come from it.
00:19
Anyway, here is the shape, right? so let's write the equation of this also.
00:23
X over 4 plus y over 2 plus z over 3 is equal to 1.
00:31
That's the equation of this tetrahedron.
00:34
So we need to look into this xy plane because it's going to give us the boundaries.
00:41
Xy plane is 2 and 4.
00:46
So the equation of this line is 2 minus 2 over 4 x over 2 x.
00:53
I mean x over 2.
00:54
Okay? so y is changing that way.
00:57
Okay, so x is changing from 0 to 4.
01:04
Y is changing from 0 to 2 minus x over 2.
01:09
And z is changing 0 to z from here.
01:13
So z from here, what is it? 3 minus 3x over 4 minus 3y over 2.
01:26
Z, dz, dy, dx.
01:31
So this is the integral to solve, but i don't know how much work we need to show for this.
01:37
This is going to be a headache if we really go through it.
01:40
So z squared over 2, right? 0 to 3 minus 3x over 4 minus 3y over 2 is equal to 1 over 2.
01:57
3 minus 3x over 4 minus 3y over 2 squared.
02:08
And now we're going to dy this.
02:13
Okay? i think the best bet is to multiply it out and plug it in and solve all that, but i think i am fair to say that use a calculator or use a computer program to solve this.
02:34
Okay? that's what i'm going to do.
02:35
I think i'm going to use wolfram for this.
02:37
So the answer is going to be nice and easy...