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A particle moves along the
x-axis with velocity

v(t)=ln(t^(2)+5t+1)". "
What is the particle's displacement between the times
t=1 and
t=5 ?
Use a graphing calculator and round your answer to three decimal places.

A particle moves along the $x$ -axis with velocity $\newline$ $v(t)=\ln \left(t^{2}+5 t+1\right) \text {. }$ $\newline$ What is the particle's displacement between the times $t=1$ and $t=5$ ? $\newline$ 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

\newline

v(t)=\ln \left(t^{2}+5 t+1\right) \text {. }

\newline

What is the particle's displacement between the times

t=1

and

t=5

?

\newline

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

Integrate Velocity Function: To find the displacement, we need to integrate the velocity function from $t=1$ to $t=5$ .
Set Up Integral: Set up the integral: $\int_{1}^{5} \ln(t^2 + 5t + 1) \, dt$ .
Evaluate Integral: Use a graphing calculator to evaluate the integral.
Calculate Displacement: After using the calculator, we get the approximate value of the integral, which is the displacement.
Approximate Displacement: The calculator shows the displacement is approximately $9.154$ .

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