Triple Integral Midpoint Rule

Problem

Approximate a triple integral over a box with the 3D midpoint rule.

grid[k][j][i] holds f sampled at the midpoint of cell (i, j, k) with uniform spacings dx, dy, dz. Sum all values and multiply by the cell volume dx * dy * dz.

Hint

This is the same averaging idea as the 2D rule, with one more nested loop.

Test cases

case 1

in: [[[[1,1],[1,1]],[[1,1],[1,1]]],0.5,0.5,0.5]

expected: 1

case 2

in: [[[[1,2],[3,4]],[[5,6],[7,8]]],1,1,1]

expected: 36

case 3

in: [[[[2]]],1,2,3]

expected: 12

case 4

in: [[],1,1,1]

expected: 0

Starter codePython

def triple_midpoint(grid, dx, dy, dz):
    # Your code here
    pass

4 test cases · run your code against them in the editor