# Tofind: the position of the particle through the given velocity.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 57RE
To determine

## Tofind:the position of the particle through the given velocity.

Expert Solution

Theposition of the particle s(t)=ln(1+t2)-Tan-1(1+t2)+π+44.

### Explanation of Solution

Given:

v(t)=2t-1(1+t2), s(0)=1 .

Concept used:

Antiderivative=integration

f(t)dt=f(t) . Or dydtdt=y .

Since, the multiplication of two operators ×ddt=1 .

Integration formula:

xndx=xn+1n+1 .

Calculation:

v(t)=2t-1(1+t2), s(0)=1 .

v(t)=2t-1(1+t2) .

v(t)=2t(1+t2)-1(1+t2).

v(t)dt=2t(1+t2)dt-1(1+t2)dt.

s(t)=ln(1+t2)-Tan-1(1+t2)+C .

s(0)=ln(1+02)-Tan-1(1+02)+C .

1=0-π4+C .

C=π4+1 .

C=π+44.

s(t)=ln(1+t2)-Tan-1(1+t2)+π+44.

Hence the position of the particle s(t)=ln(1+t2)-Tan-1(1+t2)+π+44.

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