   Chapter 5.1, Problem 6CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Checkpoint 6 Worked-out solution available at LarsonAppliedCalculus.comFind the general solution of F ' ( x ) = 4 x + 2 , and find the particular solution that satisfies the initial condition F ( 1 ) = 8.

To determine

To calculate: The general solution of F(x)=4x+2 and also the particular solution that satisfies the initial condition F(1)=8.

Explanation

Given Information:

The differential equation is F(x)=4x+2 and the initial condition is F(1)=8.

Formula used:

The sum rule of integration [f(x)+g(x)]dx=f(x)dx+g(x)dx.

The simple power rule of integration xndx=xn+1n+1+C.

Calculation:

Consider the differential equation, F(x)=4x+2.

Integrate the provided differential equation both sides.

F(x)dx=(4x+2)dx

Rewrite the above indefinite integral, use the sum integral rule, [f(x)+g(x)]dx=f(x)dx+g(x)dx.

F(x)dx=4xdx+2dx

Integrate the provided indefinite integral, use the simple power rule of integration xndx=xn+1n+1+C

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