Numerical integration

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Apply Simpson's rule with $n = 2$ subintervals (nodes at $x = -1$, $x = 1$ and $x = 3$) to approximate $\displaystyle\int_{-1}^{3} x^{3}\,dx$. Give the exact value of the estimate.

2. Warm-up

   Apply Simpson's rule with $n = 2$ subintervals (nodes at $x = 1$, $x = 5$ and $x = 9$) to approximate $\displaystyle\int_{1}^{9} x^{3}\,dx$. Give the exact value of the estimate.

3. Warm-up

   Apply Simpson's rule with $n = 2$ subintervals (nodes at $x = -3$, $x = -2$ and $x = -1$) to approximate $\displaystyle\int_{-3}^{-1} x^{3}\,dx$. Give the exact value of the estimate.

Problems shown under their original terms: Generated (template, solver-computed).