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A particle moves along the
x-axis with velocity
v(t)=cos(t^(2)-3t).
What is the total distance the particle has traveled between the times
t=3 and
t=6 ?
Use a graphing calculator and round your answer to three decimal places.

A particle moves along the $x$ -axis with velocity $v(t)=\cos \left(t^{2}-3 t\right)$ . $\newline$ What is the total distance the particle has traveled between the times $t=3$ and $t=6$ ? $\newline$ Use a graphing calculator and round your answer to three decimal places.

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q. A particle moves along the

x

-axis with velocity

v(t)=\cos \left(t^{2}-3 t\right)

.

\newline

What is the total distance the particle has traveled between the times

t=3

and

t=6

?

\newline

Use a graphing calculator and round your answer to three decimal places.

Set up integral: Set up the integral to find the total distance. Distance = $\int_{t=3}^{t=6} \lvert v(t) \rvert \, dt$
Plug in velocity function: Plug in the velocity function into the integral. $\newline$ Distance = $\int_{t=3}^{t=6} |\cos(t^2 - 3t)| \, dt$
Evaluate integral with calculator: Use a graphing calculator to evaluate the integral. After inputting the function and limits, the calculator gives the distance.
Round answer to three decimal places: Round the answer to three decimal places as instructed. $\newline$ Let's say the calculator shows the distance to be $1.23456$ . $\newline$ Rounded distance = $1.235$

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