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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find f.

f″(x) = 4 + 6x + 24x2, f(0) = 3, f(1) = 10

To determine

To find: The general antiderivative for the function f(x)=4+6x+24x2,f(0)=3,f(1)=10 .

Explanation

Given Data:

Write the given function as follows.

f(x)=4+6x+24x2,f(0)=3,f(1)=10

Formula used:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

Calculation of f(x) :

Rewrite the function f(x)=4+6x+24x2 as follows.

f(x)=4x0+6x1+24x2 (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows.

f(x)=4(x0+10+1)+6(x1+11+1)+24(x2+12+1)+C=4x+6(x22)+24(x33)+C

f(x)=4x+3x2+8x3+C

Calculation of f(x) :

Rewrite the function f(x)=4x+3x2+8x3+C as follows.

f(x)=4x1+3x2+8x3+Cx0 (2)

From the antiderivative function formula, the antiderivative for the function in equation (2) is written as follows

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