MediumCalculusca-080

Improper Integral Quadrature

Problem

Approximate the improper integral from 0 to infinity of e^(-a*x) dx by the trapezoidal rule on the truncated interval [0, t_max] with n equal subintervals.

Endpoints get weight 0.5 and interior points weight 1; multiply the weighted sum by dx = t_max / n. Assume a > 0.

Hint

The exact value is 1 / a, and the truncation error decays like e^(-a * t_max).

Test cases

case 1

in: [1,100000,50]

expected: 1.000000020833246

case 2

in: [2,100000,50]

expected: 0.5000000416666464

case 3

in: [0.5,100000,50]

expected: 2.000000010388875

case 4

in: [3,100000,50]

expected: 0.3333333958333172

Starter codePython

def improper_integral_exp(a, n, t_max):
    # Your code here
    pass

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