Mid-ordinate and Simpson's rulesAQA A-Level Further Maths: Mind map

Exam questions on Mid-ordinate and Simpson's rules

1. The integral $I=\int_0^1\frac{1}{1+x}\,dx$ is to be estimated using four strips of equal width. Let $y_r=\frac{1}{1+0.25r}$.
   Use the mid-ordinate rule with four strips to estimate $I$, to 4 decimal places.2 marks
2. The depth of a river is measured at 1 m intervals across its 6 m width. The depths, in metres, from one bank to the other are $0,\ 1.2,\ 2.0,\ 2.4,\ 1.8,\ 1.0,\ 0$. The cross-sectional area is the area under the depth profile.
   Use the mid-ordinate rule with three strips of width 2 m to estimate the cross-sectional area.2 marks
3. Consider $I=\int_0^2x^3\,dx$.
   Use Simpson's rule with two strips to estimate $I$, and show that it equals the exact value of $I$.3 marks