Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 245: 22

$1.029225$

let $f(x)$ = $sinx$ $P$ = ${x_0=o, x_1=\frac{\pi}{6}, x_2=\frac{\pi}{3}, x_3=\frac{\pi}{2}}$ $C$ = ${c_1=0.4, c_2=0.7, c_3=1.2}$ $R(f, P, C)$ = $Δx_1f(c_1)+Δx_2f(c_2)+Δx_3f(c_3)$ = $(\frac{\pi}{6}-0)(sin0.4)+(\frac{\pi}{3}-\frac{\pi}{6})(sin0.7)+(\frac{\pi}{2}-\frac{\pi}{3})(sin1.2)$ = $1.029225$