• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

### Select your language

Suggested languages for you:

Americas

Europe

Q. 6

Expert-verified
Found in: Page 361

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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

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

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

(c) The derivative of ${x}^{6}$is $\overline{)6{x}^{5}}.$

See the step by step solution

## Step 1. Given information.

The given incomplete statements are following.

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

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

(c) The derivative of ${x}^{6}$is .

## Step 1. Part (a).

derivative of ${x}^{6}.$

$\int 6{x}^{5}dx=6\left(\frac{{x}^{5+1}}{5+1}\right)+C\phantom{\rule{0ex}{0ex}}={x}^{6}+C\phantom{\rule{0ex}{0ex}}={x}^{6}$

so $\int \overline{)6{x}^{5}}dx={x}^{6}+C.$

## Step 3. Part (b).

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

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

## Step 4. Part (c)

Derivative of ${x}^{6}.$

$\frac{d}{dx}{x}^{6}=6{x}^{6-1}\phantom{\rule{0ex}{0ex}}=6{x}^{5}$

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