Calculus with Applications (10th Edition)

Published by Pearson

Chapter 7 - Integration - 7.1 Antiderivatives - 7.1 Exercises: 11

Answer

${z^4} + {z^3} + {z^2} - 6z + C$

Work Step by Step

$\begin{gathered} \int_{}^{} {\,\,\,\left( {4{z^3} + 3{z^2} + 2z - 6} \right)dz} \hfill \\ Integrate\,\,,\,\,use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{z^n}dz} = \frac{{{z^{n + 1}}}}{{n + 1}} + C \hfill \\ For\,\,each\,\,term\,,\,Then \hfill \\ = 4\,\left( {\frac{{{z^4}}}{4}} \right) + 3\,\left( {\frac{{{z^3}}}{3}} \right) + 2\,\left( {\frac{{{z^2}}}{2}} \right) - 6\,\left( z \right) + C \hfill \\ Simplify \hfill \\ {z^4} + {z^3} + {z^2} - 6z + C \hfill \\ \end{gathered}$

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