Solution
= Solution
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:
$$
\boxed{I_{1/2}=\frac12\left\{\frac12\,0^4+\left(\frac12\right)^4+\frac12\,1^4\right\}
=\frac9{32}.}
$$