00:01
So in this question we're asked to calculate the triple.
00:03
So we have the region e, which is defined as, so x, y, z, where, so, x lives between 0 and 1, y lives between 0 and x, and z lives between x into x, x into x.
00:22
So the bound is already given, and we're asked to find the integral over e.
00:28
Of the function 3yz cause of 10 x to the 5th dv right and this case be pretty easy right so we first the first integral has to be in x it's only on that's free then we integrate in y and then we integrate in z the order here is a bit irrelevant really so we're going to have 3y z cause 10 x to the 5th those will be the x and the y, actually, let's put the correct order.
01:00
So the first integral here that shows up the innermost integral is the z, then the y, then the x.
01:08
Right? so first thing, drift if we respect to z, let's just make the calculation, 0x.
01:14
So 3y, cos of 10, x to the fifth comes out.
01:18
Dift we respect to set, we're going to have a z squared over 2.
01:23
So at 2x, this will become, let's write it down so that i don't know.
01:27
Make any mistake, squared over 2 between x and 2x, and this will now be the y, the x, the x, 0 and 1, 0 and x.
01:42
So here we'll obtain 3y, cause 10x the 5th, and i'll get, when z is 2x, this will become 4x squared over 2, so 2x squared, and when z is x, this just becomes x squared over 2, the y, the x.
01:58
So 2 minus a half is going to be three halves.
02:01
So i'm going to get a three halves from here with a three.
02:04
So 9 over 2.
02:07
010x, y, cause 10x the 5th.
02:11
And from here we're going to have an x squared.
02:16
Right.
02:16
And this is the y, the x.
02:18
Now we proceed to integrate with respect to y.
02:21
So i have 9 over 2, 0 to 1...