00:01
Okay, so we want to evaluate this triple integral.
00:04
So we just need to treat every integral individually.
00:07
So the first integral we need to look at is this inner integral.
00:10
So this is a integral with respect to the z variable.
00:13
So all we need to do is treat all these here as constants.
00:16
So x and y is constants.
00:19
And just integrate with respect to z.
00:21
And i've just noticed this should be z squared.
00:25
So here we get 0 to 2, 0 to x.
00:29
And then if we integrate with respect to z squared, leaving all this as constant, we just get 3x squared y, z cubed over three, evaluated between x and minus x, and then we're left with these d y d x integrals.
00:47
So firstly, these three is cancel, and we're left with 0 to 2, 0 to x, x squared y.
00:57
Now we need to evaluate z cubed at these points, and minus x so we're left with x cubed minus minus x cubed d y d x this is zero to two zero to x squared x squared y here we still have x cubed and then we have minus x cubed so minus one cubed is minus one and then we also have this minus so this becomes a plus x cubed, d -y -d -x, then this becomes 0 to 2, 0 to x, x squared y times 2x 2x cubed, d -y -d -x, and then this is 0 to 2, 0 to x, x to the power 5, there's a 2, and we're left with y, d -y, d -x...