Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Fill in each of the blanks:
(a) $\int d x = x^{6} + C .$
(b) $x^{6}$ is an antiderivative of .
(c) The derivative of $x^{6}$ is .

(a) $\int 6 x^{5} d x = x^{6} + C .$

(b) $x^{6}$ is an antiderivative of $6 x^{5} .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given incomplete statements are following.

a) $\int d x = x^{6} + C .$

(b) $x^{6}$ is an antiderivative of .

Step 1. Part (a).

derivative of $x^{6} .$

$\int 6 x^{5} d x = 6 (\frac{x^{5 + 1}}{5 + 1}) + C = x^{6} + C = x^{6}$

so $\int 6 x^{5} d x = x^{6} + C .$

Step 3. Part (b).

As $\int 6 x^{5} d x = x^{6} + C .$

So $x^{6}$ is an antiderivative of $6 x^{5}$ .

Step 4. Part (c)

Derivative of $x^{6} .$

$\frac{d}{d x} x^{6} = 6 x^{6 - 1} = 6 x^{5}$

So derivative of $x^{6}$ is $6 x^{5} .$

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Calculus

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Short Answer

Fill in each of the blanks:
(a) $\int d x = x^{6} + C .$
(b) $x^{6}$ is an antiderivative of .
(c) The derivative of $x^{6}$ is .

Step by Step Solution

Step 1. Given information.

Step 1. Part (a).

Step 3. Part (b).

Step 4. Part (c)

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Fill in each of the blanks:(a) ∫ dx=x6+C.(b) x6 is an antiderivative of .(c) The derivative of x6is .

Step by Step Solution

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Step 1. Part (a).

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Fill in each of the blanks:
(a) $\int d x = x^{6} + C .$
(b) $x^{6}$ is an antiderivative of .
(c) The derivative of $x^{6}$ is .