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Homework Statement
Numerical integration using MATLAB m-files
Find the area under the curve of:
using trapezium rule
Homework Equations
g(x) = x^2 from x=0 to x=2
Area of a trapezium = h/2(a+b)
An M-file is a file containing code written in the MATLAB programming language. It is used to create functions and scripts that can perform specific tasks, such as solving numerical integration problems.
M-files use numerical integration algorithms to approximate the integral of a given function. These algorithms break down the integral into smaller, simpler parts and use mathematical formulas to calculate the area under the curve. The accuracy of the approximation depends on the chosen algorithm and the number of intervals used.
M-files offer a convenient and efficient way to solve numerical integration problems. They allow for the automation of complex calculations and can handle a wide range of functions. Additionally, M-files can be easily edited and customized for different integration problems.
Yes, M-files can be used for both definite and indefinite integration. Definite integration involves finding the area under a curve between two specific limits, while indefinite integration involves finding the general antiderivative of a function.
Like any numerical method, M-files have their limitations. They may not always provide an exact solution, as they rely on approximations. In some cases, they may also be computationally intensive and require a large number of intervals to achieve a desired level of accuracy.