Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 245: 20

$70$

let $f(x)$ = $2x+3$ $P$ = ${x_0=-4, x_1=-1, x_2=1, x_3=4, x_4=8}$ $C$ = ${c_1=-3, c_2=0, c_3=2, c_4=5}$ $R(f, P, C)$ = $Δx_1f(c_1)+Δx_2f(c_2)+Δx_3f(c_3)+Δx_4f(c_4)$ = $(-1-(-4))(-3)+(1-(-1))(3)+(4-1)(7)+(8-4)(13)$ = $70$