is evaluated at the center
of the box
.
Use the Midpoint Rule to estimate
,
where B is the cube defined by
.
Use partition of B into eight cubes of equal size.
What is the norm of this partition?
Solution:
The midpoints are (¼, ¼, ¼), (¼, ¼, ¾), (¼, ¾, ¼), (¾, ¼, ¼), (¼, ¾, ¾), (¾, ¼, ¾), (¾, ¾, ¼), (¾, ¾, ¾)
Thus using the midpoint rule we get :
The norm of the partition is the maximum of the lengths of the diagonals
of the cubes of the partition, which, in this case, is
.
by: gm