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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 10 and 11, find the particular solution that satisfies the differential equation and the initial condition.

f ' ( x ) = 6 x 2 + 1 ; f ( 1 ) = 9

To determine

To calculate: The particular solution that satisfied the differential equation and initial condition f(x)=6x2+1;  f(1)=9.

Explanation

Given Information:

The provided first derivative f(x)=6x2+1.

The boundary condition f(1)=9

Formula used:

The power rule of integrals:

undu=un+1n+1+C (for n1)

Here, u is function of x.

The property of Intro-differential:

df(x)dxdx=f(x)

Calculation:

Consider the derivative:

f(x)=6x2+1

Rewrite the integrand as:

df(x)dx=6x2+1

Apply, integration on both sides:

df(x)dxdx=(6x2+1)dx<

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