Double Integral Midpoint Rule

Problem

Approximate a double integral over a rectangle with the 2D midpoint rule.

grid[j][i] holds f sampled at the midpoint of cell (i, j), with uniform cell sizes dx and dy. Return the sum of all grid values times dx * dy.

Hint

Sum every cell value, then multiply once by the cell area dx * dy.

case 1

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

expected: 1

case 2

in: [[[1,2],[3,4]],1,1]

expected: 10

case 3

in: [[[0.5,1.5],[2.5,3.5]],2,0.5]

expected: 8

case 4

in: [[],1,1]

expected: 0

case 5

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

expected: 0

Starter codePython

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

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