Answer:
a)550
b)910
c)730
Step-by-step explanation:
The given model is
[tex]v(t) = 10t^2 ft/s[/tex]
Use the interval [0,6], with n=6 rectangles
Then, the interval width is
[tex]\Delta t = \frac{b-a}{n}[/tex]
[tex]\Delta t = \frac{6-0}{6}[/tex]= 1
so, the sub intervals are
[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]
Now evaluating the function values
[tex]f(t_0)= f(0) = 0[/tex]
[tex]f(t_1)= f(1) = 10[/tex]
[tex]f(t_2)= f(2) = 40[/tex]
[tex]f(t_3)= f(3) = 90[/tex]
[tex]f(t_4)= f(4) = 160[/tex]
[tex]f(t_5)= f(5) = 250[/tex]
[tex]f(t_6)= f(6) = 360[/tex]
a) left hand sum is
L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]
=[tex]1 [0+ 10+40+90+160+250][/tex]
= 550
b) right hand sum
R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]
= [tex]1 [10+40+90+160+250+360][/tex]
= 910
c) average of two sums is
[tex]\frac{L_5+R_5}{2}[/tex]
= [tex]\frac{550+910}{2}[/tex]
=730
