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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

True or False? In Exercises 73-78, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

If f ' ( x ) = g ( x ) , then g ( x ) d x = f ( x ) + C .

To determine
Whether the statement “There is only one anti-derivative for a polynomial whose graph passes through the origin.” is true or false.

Explanation

Consider a polynomial of degree n.

p(x)=anxn+an1xn1++a0.

Here, an0.

The anti-derivative of this polynomial would be:

p(x)dx=(anxn+an1xn1++a0)dx=anxndx+an1xn1dx++a0

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