00:01
In the question we have, we have a solid bounded by coordinates, bounded by coordinates plane that is x is equal to 0, y is equal to 0 and z is equal to 0 and we have 2x plus 3y plus 6z is equal to 12.
00:45
So z varies 0 to 1 by 6, 12 minus 2x minus 3y and y varies 0 to 1 by 3 multiply by 12 minus 2x and x varies 0 to 6.
01:18
Therefore, volume will be equal to triple integration of dx, dy, dz and here the limit is from 0 to 1 by 6 multiply by 12 minus 2x minus 3y and here the limit is from 0 to 1 by 3 multiply by 12 minus 2x and here the limit is from 0 to 6.
01:49
So, this will further equal to double integration of z and the limit is from 0 to 1 by 6 multiply by 12 minus 2x minus 3y, dy, dx here the limit is from 0 to 1 by 3 multiply by 12 minus 2x, here the limit is from 0 to 6.
02:18
This is further equal to double integration and we are putting here upper limit minus lower limit.
02:25
So, we will get 1 by 6 multiply by 12 minus 2x minus 3y, dy, dx here the limit is from 0 to 1 by 3 multiply by 12 minus 2x, here the limit is from 0 to 6.
02:40
So, this is further equal to 1 by 1 by 6 integration of 12 minus 2x minus 3y whole square upon 2 multiply by minus 3 and the limit is from 0 to 1 by 3 multiply by 12 minus 2x, dx limit is from 0 to 6.
03:04
So, this is further equal to minus 1 upon 36 integration of 12 minus 2x minus 3 multiply by 1 by 3 multiply by 12 minus 2x whole square minus 12 minus 2x whole square, dx and the limit is from 0 to 6.
03:30
So, this is further equal to minus 1 upon 36 integration of 12 minus 2x minus 12 plus 2x whole square minus 12 minus 2x whole square, dx and the limit is from 0 to 6...