Question

Write a program that uses the composite trapezoidal rule or the composite Simpson rule to implement the reduction approach outlined above to approximate.

a) Python
b) Java
c) C++
d) MATLAB

Answer 1

The composite trapezoidal rule and the composite Simpson rule are methods used in numerical integration to approximate the definite integral of a function. These methods involve dividing the interval of integration into smaller subintervals and applying either the trapezoidal rule or the Simpson rule to each subinterval.

Step-by-step explanation:

The composite trapezoidal rule and the composite Simpson rule are methods used in numerical integration to approximate the definite integral of a function. These methods involve dividing the interval of integration into smaller subintervals and applying either the trapezoidal rule or the Simpson rule to each subinterval. By summing the individual approximations, we can get a better approximation of the integral.

In Python, the 'scipy' library provides functions like 'trapz()' and 'simps()' that can be used to implement these methods. In Java, C++, and MATLAB, you can create your own functions to apply the trapezoidal or Simpson rule to calculate the integral.

Here's an example of how you can implement the composite trapezoidal rule in Python:

from scipy import integrate

def f(x):
return x**2

a = 0
b = 2
n = 100

x = np.linspace(a, b, n+1)
h = (b-a)/n

integral = np.sum(f(x[1:]) + f(x[:-1])) * h/2
print(integral)