Chapter 8 - Techniques of Integration - 8.9 Numerical Integration - Preliminary Questions - Page 457: 4

$$0.28125$$

Given $$\int_0^3f(x)dx,\ \ |f''(x)|=2 $$ Since the maximum error is $$ \left|f^{\prime \prime}(x)\right| \frac{(b-a)^{3}}{12 n^{2}}$$ Then \begin{align*} \left|f^{\prime \prime}(x)\right| \frac{(b-a)^{3}}{12 n^{2}}&\leq2 \frac{(3-0)^{3}}{12 (4)^{2}}\\ &=\leq 0.28125 \end{align*}