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First correct answer will get full rating, thanks! A particle that moves along a

ID: 3341817 • Letter: F

Question



First correct answer will get full rating, thanks!

A particle that moves along a straight line has velocity v(t) = t2e-4tm/s after t seconds. This problem involves determining the distance x(t) that it will travel during the first t seconds. Use integration by parts once with u = t2 and dv = e-4tdt to begin determining the indefinite integral (ant derivative) of t2e-4t . This gives Use integration by parts again to complete finding the indefinite integral (ant derivative) of t2e-4t. This gives Use the initial condition (IC) that x(0) = 0 to determine the value of the constant C: Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: x(t) =

Explanation / Answer

1) -t^2 * e^(-4t) / 4 and   te^(-4t)/ 2

2) -t^2 * e^(-4t) / 4 - te^(-4t) / 8 - e^(-4t) / 32 + C


3) C = 1/32

4) -t^2 * e^(-4t) / 4 - te^(-4t) / 8 - e^(-4t) / 32 + 1/32