00:01
Okay, we want to integrate 6xy over some volume, and the volume is described over here.
00:08
And because it tells us this and this, we don't really have to draw the volume because it's saying go from z equals zero, which is the xy plane, to this z.
00:19
Okay, so that's what's going to be on the inside here.
00:22
0 to 1 plus x plus y, 6x, dz.
00:29
So all we really have to do is look in the xy plane and see what we're looking at.
00:34
Okay, y equals the square root of x, goes through 0 ,0, 1, 4, 2.
00:43
Okay, so it looks like a parabola on its side.
00:47
Y equals zero, that's the x -axis, and then x equals 1.
00:54
All right, so i think i would do d, y first, and i would go 0 to the square root of x, and then x will go from here zero pile them up until they get to one zero to one d x all right let's see if you can integrate that it's zero to one zero to the square root of x there's no z here so six x y is a constant so we just have to stick a z to it x plus y x x 6x y times 1 plus x plus y minus 0 okay i think you're gonna have to multiply the 6x y in there before you can integrate so let's do that 6x y times 1 plus 6x squared y plus 6x y plus 6x y squared okay now we're integrating with respect to y so the first one will be 6x y squared over 2 so 3x y squared and the next one will be 6 x y squared and the next one will be 6 x squared y squared over 2 so 3 x squared y squared and the last one will be 6x y cubed over 3 x y cubed 0 2 square root of x so 0 to 1 3x square root of x squared that's x plus 3x squared square root of x squared that's x plus 2x squared square root of x to the third power, i'm calling it, call that x to the three halves.
03:19
Minus zero, zero, zero.
03:23
Okay, this one is three x squared, so it's integral three x cubed over three...