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Year 2 of the mathematics course of the University of Oxford

Options I course of the University of Oxford

Past exam of the options I course of the University of Oxford

2012

For one interval, the <trapezoidal rule> gives
$$
\boxed{I_1=\frac12\{0^4+1^4\}=\frac12.}
$$
For two intervals of width $h=1/2$, the composite <trapezoidal rule> gives half weights at the endpoints and full weight at the internal node:
$$
\boxed{I_{1/2}=\frac12\left\{\frac12\,0^4+\left(\frac12\right)^4+\frac12\,1^4\right\}
=\frac9{32}.}
$$

Solution

Past exam of the options I course of the University of Oxford / 2012 / P / P2 / b / Solution

Past exam of the options I course of the University of Oxford / 2012 / P / P2 / b / Solution

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Past exam of the options I course of the University of Oxford / 2012 / P / P2 / b / Solution

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