   Chapter 3.9, Problem 7E

Chapter
Section
Textbook Problem

# Find the most general antiderivative of the function. (Check your answer by differentiation.) f ( x ) = 7 x 2 / 5 + 8 x − 4 / 5

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=7x25+8x-45

4) Calculation:

The given function is fx=7x25+8x- 45

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,

7x25+125+1+8 x-4 5 +1-45+1 +C

To simplify 25+1

The common denominator is 5

Therefore it becomes,25+55

Which gives 75

Similarly,-45+1   becomes

-45+55= 15

Thus it gives,

7x7575 +8 x1515+C

Therefore,

7·57 x75+8·51 &#

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