Chapter 4: Q. 7 (page 361)

Fill in each of the blanks:
(a) $\int x^{6} d x = + C .$
(b) is an antiderivative of role="math" localid="1648619282178" $x^{6} .$
(c) The derivative of is $x^{6} .$

Short Answer

Expert verified

(a) $\int x^{6} d x = \frac{x^{7}}{7} + C .$

(b) $\frac{x^{7}}{7}$ is an antiderivative of $x^{6} .$

Step by step solution

Step 1. Given information.

The given incomplete statements are following.

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

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

Step 1. Part (a).

integral of $x^{6}$

$\int x^{6} d x = (\frac{x^{6 + 1}}{6 + 1}) + C = \frac{x^{7}}{7} + C$

so $\int x^{6} d x = \frac{x^{7}}{7} + C .$

Step 3. Part (b).

As $\int x^{6} d x = \frac{x^{7}}{7} + C .$

So $\frac{x^{7}}{7}$ is an antiderivative of $x^{6} .$

Step 4. Part (c)

antiderivative of $x^{6} .$

role="math" localid="1648620114580" $\int x^{6} d x = (\frac{x^{6 + 1}}{6 + 1}) + C = \frac{x^{7}}{7} + C$

so The derivative of $\frac{x^{7}}{7}$ is $x^{6} .$

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Fill in each of the blanks:
(a) $\int x^{6} d x = + C .$
(b) is an antiderivative of role="math" localid="1648619282178" $x^{6} .$
(c) The derivative of is $x^{6} .$

Short Answer

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) ∫x6dx=+C.(b) is an antiderivative of role="math" localid="1648619282178" x6.(c) The derivative of is x6.

Short Answer

Step by step solution

Step 1. Given information.

Step 1. Part (a).

Step 3. Part (b).

Step 4. Part (c)

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Fill in each of the blanks:
(a) $\int x^{6} d x = + C .$
(b) is an antiderivative of role="math" localid="1648619282178" $x^{6} .$
(c) The derivative of is $x^{6} .$