Numerical Methods Coursework

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Paul Koleoso        30083490

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

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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 shapes such as rectangles which approximately covers the area. I intend to use the trapezium and Mid-point rule as these are on of the basis in which the approximation can be found.

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Note: X is in radians.

  1. Mid – point rule: The mid point rule was adopted, because it is used to approximate the area underneath the graph using rectangles. Below is the formula which is involved in the calculation.

 

  1. Trapezium rule; This is also similar to the mid – point rule. It was adopted,       because it would help me to approximate the region under the graph using strips of ...

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