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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 the most general antiderivative of the function. (Check your answer by differentiation.)

f(x) = x(12x + 8)

To determine

To find: The most general antiderivative of the function f(x)=x(12x+8) and check the determined antiderivative for the function f(x)=x(12x+8) by differentiation.

Explanation

Given Data:

Write the given function as follows.

f(x)=x(12x+8)

Formula used 1:

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

Here, C is the constant.

Formula used 2:

Calculation:

Write the required differentiation formula to verify the answer as follows.

ddx(xn)=nxn1ddx(constant)=0

Rewrite the function f(x)=x(12x+8) as follows.

f(x)=12x2+8x1 (1)

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

F(x)=12(x2+12+1)+8(x1+11+1)+C=12(x33)+8(x22)+C=4x3+4x2+C

Thus, the most general antiderivative of the function f(x)=x(12x+8) is 4x3+4x2+C_

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