Question

not working, would you mind checking the code please? def EulerIntegrate(lower, upper, step_size, iterations=1000): integral = 0 x = lower y = cosh(x) while x < upper: x += step_size y = cosh(x) integral += y return integral lower_bound = 0.00001 upper_bound = 0.1 error = 1e-3 while abs(calculated_integral - analytical_integral) > error: step_size = (lower_bound + upper_bound) / 2 calculated_integral = EulerIntegrate(-1, 1, step_size) if calculated_integral > analytical_integral: upper_bound = step_size else: lower_bound = step_size

Answer 1

The code provided by the student is designed to perform numerical integration using Euler's method on the cosh(x) function. The issues include incorrect calculation of the integral in each step and the missing initial value for 'analytical_integral'. Corrections include adjusting the integration approach and defining 'analytical_integral' before the loop.

Step-by-step explanation:

The student's question pertains to debugging a Python function designed to perform numerical integration using Euler's method. The function is intended to approximate the integral of the hyperbolic cosine function (cosh(x)) over a specified interval. However, the student has encountered an issue where the code is not functioning as expected.

The primary issue with the provided code is that the EulerIntegrate function is designed to calculate the integral in a forward stepping manner, but it does not properly account for the area beneath the curve in each step. Furthermore, the main while loop, which is supposed to refine the step size, is missing a crucial assignment of 'analytical_integral' before the loop begins.

To fix the issue, we need to modify the EulerIntegrate function to correctly calculate the area of each segment using the midpoint or trapezoidal rule, and also ensure that the variable 'analytical_integral' is set to the actual value obtained from the analytical integration of 'cosh(x)' over the interval [-1, 1] before the loop starts.