Simpson's ruleEdexcel A-Level Further Maths: Mind map

Exam questions on Simpson's rule

1. Simpson's rule with 4 strips is used to estimate $\int_{0}^{2}f(x)\,dx$. The values of $f(x)$ at $x=0,\ 0.5,\ 1,\ 1.5,\ 2$ are $1,\ 3,\ 4,\ 6,\ 7$ respectively.
   The exact value of the integral is $8.7$. Find the percentage error in the Simpson's rule estimate, giving your answer to 3 significant figures.2 marks
2. Simpson's rule is used with 4 strips to estimate $\int_{2}^{10}f(x)\,dx$. The values of $f(x)$ at $x=2,\ 4,\ 6,\ 8,\ 10$ are $3,\ 5,\ 8,\ 12,\ 17$ respectively.
   Use the values to find the Simpson's rule estimate of the integral, giving your answer to 3 significant figures.2 marks
3. Let $I=\int_{0}^{1}\frac{4}{1+x^{2}}\,dx$, whose exact value is $\pi$. A calculator may be used.
   Use Simpson's rule with 4 strips to estimate $I$, giving your answer to 5 significant figures.3 marks