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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding a Particular Solution In Exercises 43–50, find the particular solution that satisfies the differential equation and the initial condition. See Example 6.

f ' ( x ) = 3 x 2 + 4 ; f ( 1 ) = 6

To determine

To calculate: The particular solution of differential equation f'(x)=3x2+4 with initial condition f(1)=6.

Explanation

Given Information:

The differential equation is f'(x)=3x2+4 and the initial condition is f(1)=6.

Formula used:

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

Calculation:

Consider the differential equation, f'(x)=3x2+4.

Integrate the provided differential equation, use the simple power rule of integration xndx=xn+1n+1+C.

f'(x)dx=(3x2+4)dxf(x)=3x2dx+4dx=3(x2+12+1)+4x+C=x3+4x+C

The provided initial condition is f(1)=6

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