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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

1 Answer

6 votes

Answer:

a)550

b)910

c)730

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 = (b-a)/(n)


\Delta t = (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


(L_5+R_5)/(2)

=
(550+910)/(2)

=730

User Tom Pietrosanti
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