   Chapter 3.R, Problem 53E

Chapter
Section
Textbook Problem

# 53-54 Find the most general antiderivative of the function. f ( x ) = 4 x − 6 x 2 + 3

To determine

To find:

The most general antiderivative of thegiven function.

Solution:Fx=83x32-2x3+3x+c

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 f for all x in I.

2) Formula:

Power rule of antiderivative;ddxxn+1n+1=xn

3) Given:

fx=4x-6x2+3

4) Calculation:

Here  fx=4x-6x2+3

It can be written as, fx=4x12-6x2+3

Find the general antiderivative F using, power rul

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