Asked by Anonymous
Your velocity is given by v(t)=1 t2+2 in m/sec, with t in seconds. Estimate the distance, s, traveled between t=0 and t=8. Use the average of the left and right sums with 4 subdivisions.
Answers
Answered by
Damon
I assume you mean
v(t) = t^2 + 2
I am not going to do the four trapezoids for you but I will do the integral so you know if you have done the area right.
s(t) = (1/3) t^3 + 2 t + c
when t = 0, let s = 0 so let c = 0
(we could chose any old starting s and resulting constant c because we subtract the first from the last in the end anyway)
s(8) = (1/3)(512)+ 16 = 186 2/3
s(0+ = 0 so
186 2/3 is the exact answer
now you need to do
[v(0) + v(2)] * (1/2)* (2) +
[v(2) + v(4)] +
[v(4) + v(6)] +
[v(6) + v(8)]
= answer
by the way that is
[v(0) + 2v(2) + 2v(4)+2v(6)+v(8)]
v(t) = t^2 + 2
I am not going to do the four trapezoids for you but I will do the integral so you know if you have done the area right.
s(t) = (1/3) t^3 + 2 t + c
when t = 0, let s = 0 so let c = 0
(we could chose any old starting s and resulting constant c because we subtract the first from the last in the end anyway)
s(8) = (1/3)(512)+ 16 = 186 2/3
s(0+ = 0 so
186 2/3 is the exact answer
now you need to do
[v(0) + v(2)] * (1/2)* (2) +
[v(2) + v(4)] +
[v(4) + v(6)] +
[v(6) + v(8)]
= answer
by the way that is
[v(0) + 2v(2) + 2v(4)+2v(6)+v(8)]
Answered by
Jack
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