Question

A model rocket has upward velocity v(t) = 10t2 ft/s, t seconds after launch. Use the interval [0, 6] with n = 6 and equal subintervals to compute the following approximations of the distance the rocket traveled. (Round your answers to two decimal places.
(a) Left-hand sum = _____ ft
(b) Right-hand sum = _____ ft
(c) average of the two sums = ______ ft

Answer 1

Answer:

a)550

b)910

c)730

Step-by-step explanation:

The given model is

$v(t) = 10t^2 ft/s$

Use the interval [0,6], with n=6 rectangles

Then, the interval width is

$\Delta t = \frac{b-a}{n}$

$\Delta t = \frac{6-0}{6}$= 1

so, the sub intervals are

[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]

Now evaluating the function values

$f(t_0)= f(0) = 0$

$f(t_1)= f(1) = 10$

$f(t_2)= f(2) = 40$

$f(t_3)= f(3) = 90$

$f(t_4)= f(4) = 160$

$f(t_5)= f(5) = 250$

$f(t_6)= f(6) = 360$

a) left hand sum is

L_6 = $\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)]$

=$1 [0+ 10+40+90+160+250]$

= 550

b) right hand sum

R_6 = $\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)]$

= $1 [10+40+90+160+250+360]$

= 910

c) average of two sums is

$\frac{L_5+R_5}{2}$

= $\frac{550+910}{2}$

=730