   Chapter 3.9, Problem 2E

Chapter
Section
Textbook Problem

# Find the most general antiderivative of the function. (Check your answer by differentiation.) f ( x ) = x 2 − 3 x + 2

To determine

To find:

The most general antiderivative of the given function.

Explanation

1) Concept:

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is,Fx+C where C  is an arbitrary constant.

Definition:

A function F  is called an antiderivative of f on an interval I if

F'x=fx for all x in I.

2) Formula:

Power rule of antiderivative

ddx xn+1n+1=xn

3) Given:

fx=x2-3x+2

4) Calculation:

The given function is fx=x2-3x+2

To find the most general antiderivative of f, use the power rule of antiderivative.

Power rule of antiderivative

ddx xn+1n+1=xn

Which gives,

x2+12+1-3x1+11+1+2x0+10+1+C

Simplifying this,

x33-3x22+2x1+C

13 x3-32 x2+2x+C

Therefore, the most general antiderivative is

Fx=13 x3-32 x<

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