Question
A particle that moves along a straight line has velocity
v(t)=t^2 e^-4t
meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
v(t)=t^2 e^-4t
meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
Answers
Bot
The answer is: (1/3)e^-4t(t^3 + 3t^2 + 6t + 6) meters.
oobleck
AAAaannndd the bot gets it wrong yet again!
s(t) = ∫[0,t] x^2 e^(-4x) dx
= 1/32 (1 - (8t^2+4t+1)e^(-4t))
s(t) = ∫[0,t] x^2 e^(-4x) dx
= 1/32 (1 - (8t^2+4t+1)e^(-4t))