Chapter 4: Q. 6 (page 361)

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

Short Answer

Expert verified

(a) $鈭� 6 x^{5} d x = x^{6} + C .$

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

Step by step solution

Step 1. Given information.

The given incomplete statements are following.

a) $鈭� d x = x^{6} + C .$

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

Step 1. Part (a).

derivative of $x^{6} .$

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

so $鈭� 6 x^{5} d x = x^{6} + C .$

Step 3. Part (b).

As $鈭� 6 x^{5} d x = x^{6} + C .$

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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91影视

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

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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91影视

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

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

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

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