Question Number 224078 by OmoloyeMichael last updated on 18/Aug/25
$$\boldsymbol{{Evaluate}}\:\underset{\mathrm{0}} {\int}^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{sinxdx}}\:\boldsymbol{{with}}\:\boldsymbol{{h}}=\frac{\boldsymbol{\pi}}{\mathrm{12}},\boldsymbol{{correct}}\:\boldsymbol{{to}} \\ $$$$\mathrm{5}\:\boldsymbol{{decimal}}\:\boldsymbol{{places}},\boldsymbol{{using}} \\ $$$$\left(\mathrm{1}\right)\boldsymbol{{Trapezoidal}}\:\boldsymbol{{rule}} \\ $$$$\left(\mathrm{2}\right)\boldsymbol{{Newton}}−\boldsymbol{{Cotes}}\:\boldsymbol{{formula}}\:\boldsymbol{{for}}\:\boldsymbol{{n}}=\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\boldsymbol{{Simpson}}\:\mathrm{3}/\mathrm{8}\:−\boldsymbol{{rule}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{truncation}}\:\boldsymbol{{error}}\:\boldsymbol{{in}}\:\boldsymbol{{each}}\:\boldsymbol{{case}}. \\ $$