3 The extension, , of a material with an applied force, , is given by .
a) Calculate the work done if the force increases from 200N to 600N using:
i) An analytical integration technique
ii) A numerical integration technique
[Note: the work done is given by the area under the curve]
b) Compare the two answers
c) Using a computer spreadsheet increase the number of values used for your numerical method
d) Analyse any affect the size of numerical step has on the result.
If we get F, is given by y = e^F x 1 x 10^-3. (e is to the power of F x 1 x 10; 10 is to the power of -3 in that equation)
ii)Solving by Trapezoidal Rule
According to Trapezoidal rule
B)Answer obtained in part(ii) is lesser than that obtained in part(i).
C)If we increase the values of n to n=5,n=6,n=7...The obtained Answer is closer to the actual value.
D)As n becomes larger and larger,the more accurate the answer is.