You have a definite integral to compute: ∫[a, b] f(x)dx, where f(x) is the integrand, and a and b are the integration limits.
Select an integration method, such as the Trapezoidal Rule or Simpson's Rule, based on the desired level of accuracy.
Use the selected integration method to approximate the integral value. The formulas are as follows:
Trapezoidal Rule:
∫[a, b] f(x)dx ≈ h/2 [f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]
Simpson's Rule:
∫[a, b] f(x)dx ≈ h/3 [f(a) + 4f(a+h) + 2f(a+2h) + 4f(a+3h) + ... + 2f(b-h) + 4f(b-2h) + f(b)]
Here, h is the step size, which determines the width of the subintervals used in the approximation.
You can assess the accuracy of the numerical integration method by considering the error and comparing results obtained with different step sizes.
The result of the chosen integration method provides an approximation of the definite integral.
These methods are essential for approximating integrals when an analytical solution is not readily available.