Answer:
Step-by-step explanation:
[tex]\int\limits^2_0 {(x^2-4x)} \, dx[/tex] n=8 f(x) = x² - 4x
convert [0,2] into 8 subintervals
width of each interval is
[tex]\delta x =\frac{2-0}{8}=0.25[/tex]
All subintervals are:
[0, 0.25], [0.25, 0.5], [0.5, 0.75], [0.75, 1], [1, 1.25], [1.25, 1.5], [1.5, 1.75] and [1.75, 2]
Let, [tex]x_i[/tex] be the right end point of each interval i=1,..8
[tex]x_1=0.25, x_2=0.5, x_3=0.75, x_4=1, x_5=1.25, x_6=1.5, x_7=1.75, x_8=2[/tex]
Reiman sum is
[tex]R_8=\delta x[f(x_1)+f(x_2)+...f(8)]\\\\0.25[f(0.25)+f(0.5)+...+f(2)]\\\\0.25\times[-23.25]\\=-5.8125[/tex]
