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Q. 6

Expert-verifiedFound in: Page 361

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 __$\overline{)6{x}^{5}}.$__

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__ __.

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

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

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

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 $\overline{)6{x}^{5}}.$

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