   Chapter 4.9, Problem 38E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find f.f′(t) = 3t − 3/t, f(1) = 2, f(−1) = 1

To determine

To find: The general antiderivative for the function f(t)=3t3t,f(1)=2,f(1)=1 .

Explanation

Given Data:

Write the given function as follows.

f(t)=3t3t,f(1)=2,f(1)=1

Formula used:

The antiderivative function for the function ax is axlna+C .

Here, C is the constant.

The antiderivative function for the function 1t is ln|t|+C .

Calculation of f(t) :

Rewrite the function f(t)=3t3t as follows.

f(t)=3t3(1t) (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows.

f(t)=3tln(3)3ln|t|+C (2)

As f(1)=2 , substitute 1 for t in equation (2),

f(1)=31ln(3)3ln|1|+C=3ln(3)0+C=3ln(3)+C

Rewrite the expression as follows

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