A particle that moves along a straight line has velocity v(t) = te "m/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. %3D Step 1. Use integration by parts once with u = t² and dv = e "dt to begin determining the indefinite integral (antiderivative) of t²e 4 This gives Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of te M This gives Step 3. Use the initial condition (IC) that æ(0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: #(t)
A particle that moves along a straight line has velocity v(t) = te "m/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t seconds. %3D Step 1. Use integration by parts once with u = t² and dv = e "dt to begin determining the indefinite integral (antiderivative) of t²e 4 This gives Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of te M This gives Step 3. Use the initial condition (IC) that æ(0) = 0 to determine the value of the constant C: Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: #(t)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A particle that moves along a straight line has velocity v(t) = te "m/s after t seconds. This problem involves determining the distance (t) that it will travel during the first t
seconds.
%3D
Step 1. Use integration by parts once with u = t² and dv = e "dt to begin determining the indefinite integral (antiderivative) of t²e 4 This gives
Step 2. Use integration by parts again to complete finding the indefinite integral (antiderivative) of te M This gives
Step 3. Use the initial condition (IC) that æ(0) = 0 to determine the value of the constant C:
Step 4. Combine the results of steps 2 and 3 above to determine the distance the particle will travel during the first t seconds: #(t)
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