MediumCalculusca-301

Midpoint versus Trapezoid Estimate

Problem

Compare the composite midpoint and trapezoidal rules on n equal subintervals of [a, b] for a polynomial: the midpoint rule samples at subinterval centers, the trapezoid rule at the nodes.

Return [midpoint, trapezoid].

Hint

Midpoint uses (i + 0.5) * h; trapezoid sums interior nodes with full weight.

Test cases

case 1

in: [[0,0,1],0,1,2]

expected: [0.3125,0.375]

case 2

in: [[1],0,2,4]

expected: [2,2]

case 3

in: [[0,0,0,1],0,2,2]

expected: [3.5,5]

Starter codePython

def midpoint_versus_trapezoid(coeffs, a, b, n):
    # Your code here
    pass

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