Finding a Riemann Sum

Question

Find the Riemann Sum for f(x)=x^2 +3x over the interval [0,8] where

x0=0 x1=1 x2=3 x3=7 x4=8

and

c1=1 c2=2 c3=5 c4=8

Answer 1

f(x) = x² + 3x

Riemann Sum: f(c₁)(length of first interval) + f(c₂)(length of second interval) + f(c₃)(length of third interval) + f(c₄)(length of fourth interval)

= f(1)(1-0) + f(2)(3-1) + f(5)(7 - 3) + f(8)(8 - 7)