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MATH2167: Trapezoidal Rule - Simpson’s 1/3 rd Rule - Mathematics Assessment Answer
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Subject Code: MATH2167
Internal Code: 6CIGJ
2. Estimate the area of the base of the land (quadrilateral), you sketched in (1), by using trapezoidal rule and Simpson’s 1/3 rd rule with any number of strips (at least 8 strips) of your choice.
3. Now join the two end points of sides a, b, c and d of the quadrilateral you sketched in part (1), by irregular curves (an example is shown in Fig 2.) to create the land of your choice named Student Land.
Now estimate these four areas (areas you sketched outside the four sides a, b, c and d of the quadrilateral) by using trapezoidal rule with 9 strips (if addition of your student number is an odd number) or by using Simpson’s 1/3 rd rule with 10 strips (if addition of your student number is an even number). Hence estimate the total area of the land and conclude your findings.
PART II: Trapezoidal Rule and Simpson’s 1/3 rd Rule in finding approximate volume
For transportation purposes undersea tunnel needs to be constructed to provide fast link between the Student Land and X-Land, see Figure 3.
A tunnel of length (1000)unita? (similar to the Fig 4.) will be constructed to join the Student Land with X-Land. The eleven cross sectional areas at regular intervals are: 2units
Now estimate the volume of the undersea tunnel by using a trapezoidal rule with 10 strips and by using Simpson’s 1/3 rd rule with 10 strips. Comment on your findings.
Mathematics Assessment Answer
TASK: Trapezoidal rule and or Simpson’s 1/3 rd rule are commonly used to find the approximate surface area of the lands or some irregular surfaces. In this project you need to design a small land of your choice. Then you need to find the area and volume by using Trapezoidal rule and or Simpson’s 1/3 rd rule as indicated below. 1. To sketch the design of the project first you draw a quadrilateral (base of your land as shown in Fig 1.) with side lengths of a , b, c and d units on a graph paper, where a = 600 units + last 3 digits of your student number b = 450 units + last 3 digits of your student number c = 400 units + last 2 digits of your student number d = 350 units + last 2 digits of your student number (e.g. if your student number is 3654283 then a = 883, b = 733, c = 483, d = 433 units respectively).
2. Estimate the area of the base of the land (quadrilateral), you sketched in (1), by using trapezoidal rule and Simpson’s 1/3 rd rule with any number of strips (at least 8 strips) of your choice.
3. Now join the two end points of sides a, b, c and d of the quadrilateral you sketched in part (1), by irregular curves (an example is shown in Fig 2.) to create the land of your choice named Student Land.
Now estimate these four areas (areas you sketched outside the four sides a, b, c and d of the quadrilateral) by using trapezoidal rule with 9 strips (if addition of your student number is an odd number) or by using Simpson’s 1/3 rd rule with 10 strips (if addition of your student number is an even number). Hence estimate the total area of the land and conclude your findings.
PART II: Trapezoidal Rule and Simpson’s 1/3 rd Rule in finding approximate volume
For transportation purposes undersea tunnel needs to be constructed to provide fast link between the Student Land and X-Land, see Figure 3.
A tunnel of length (1000)unita? (similar to the Fig 4.) will be constructed to join the Student Land with X-Land. The eleven cross sectional areas at regular intervals are: 2units
Now estimate the volume of the undersea tunnel by using a trapezoidal rule with 10 strips and by using Simpson’s 1/3 rd rule with 10 strips. Comment on your findings.
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