   Chapter 3.9, Problem 22E

Chapter
Section
Textbook Problem

# 21-22 Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f ( x ) = x + 2 sin x ,    F ( 0 ) = − 6

To determine

To find:

The antiderivative F  of f that satisfies the given condition

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) Given:

fx=x+2sinx, F0=-6

3) Calculations:

Here fx=x+2sinx

Find the general antiderivative F using the power rule of antiderivative

Fx=x22-2(-cosx)+c

Fx=x22+2cosx+c

Here F0=-6

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 