`v(t) = 2t - 1/(1 + t^2), s(0) = 1` A particle is moving with the given data. Find the position of the particle.

Textbook Question

Chapter 4, Review - Problem 73 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`v(t)=2t-1/(1+t^2)`

position of the particle s(t) is given by,

`s(t)=intv(t)dt`

`s(t)=int(2t-1/(1+t^2))dt`

`s(t)=2(t^2/2)-arctan(t)+C` , C is constant

`s(t)=t^2-arctan(t)+C`  

Now let's find C , given s(0)=1

`s(0)=1=0^2-arctan(0)+C`

`1=0-0+C`

`C=1`

position of the particle is given by,

`s(t)=t^2-arctan(t)+1`

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