Science:Math Exam Resources/Courses/MATH101/April 2012/Question 07 (b)

MATH101 April 2012

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Question 07 (b)
Let $I=\int _{1}^{2}(1/x)\,dx$. Write down the Simpson's approximation S4 for I. You do not need to simplify your answer.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
The formula for the Simpson's rule is given by $S_{n}:={\frac {\Delta x}{3}}\left(f(x_{0})+4f(x_{1})+2f(x_{2})+...+4f(x_{n-1})+f(x_{n})\right)$ where $n$ is an even integer.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The Simpson's rule approximation for $n=4$ is given by: $S_{4}={\frac {\Delta x}{3}}\left(f(x_{0})+4f(x_{1})+2f(x_{2})+4f(x_{3})+f(x_{4})\right)$ In our situation, $\Delta x={\frac {1}{4}}$, $f(x)={\frac {1}{x}}$, $\displaystyle x_{0}=1$ and $\displaystyle x_{4}=2$. Thus we can calculate $S_{4}$ as: $S_{4}={\frac {1/4}{3}}\left({\frac {1}{1}}+4{\frac {1}{5/4}}+2{\frac {1}{6/4}}+4{\frac {1}{7/4}}+{\frac {1}{2}}\right)$

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