Numerical Methods Coursework

This essay hasn't yet been marked by one of our teachers

You can view 3 essays on Core & Pure Mathematics that have been Marked by Teachers

The first 200 words of this essay...

For this coursework, I am going to use knowledge of numerical methods to produce an approximation to an area which does not have an analytic solution.

Problem

.

I would be finding the approximation of the integral on the graph between the shaded portion of the graph above which is from 0 to 1 using numerical integration.

This problem was chosen because it cannot be integrated by any analytical method, therefore approximation method would be used. Due to this I suggest that this problem will be appropriate for numerical solution.

Strategy

To solve this problem, I am going to use knowledge of numerical integration studied in the Numerical Methods textbook.

Numerical integration is a method used to approximate an area under the graph. According to syllabus on NM module, the approximate methods of definite integrals may be determined by numerical integration using;

1. Mid - point rule

2. Trapezium rule

3. Simpson's rule

Since there are lots mathematical functions which can not be integrated in real life, an alternative approach to these problems are to sub-divide the area under the graph into strips or