To calculate the error, we will use M = 64 ⋅ 4800 {\displaystyle M=64\cdot 4800} and hence, we want Error ≤ M 12 ( b − a ) 3 n 2 ≤ 64 ⋅ 4800 12 4 3 n 2 ≤ 64 ⋅ 400 64 n 2 ≤ 64. {\displaystyle {\text{Error}}\leq {\frac {M}{12}}{\frac {(b-a)^{3}}{n^{2}}}\leq {\frac {64\cdot 4800}{12}}{\frac {4^{3}}{n^{2}}}\leq 64\cdot 400{\frac {64}{n^{2}}}\leq 64.} This means we need n 2 ≥ 64 ⋅ 400 {\displaystyle n^{2}\geq 64\cdot 400} , so n ≥ 8 ⋅ 20 = 160 {\displaystyle n\geq 8\cdot 20=160} . Therefore, we can take n = 160 {\displaystyle n=160} .
