Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 43

Answer

\[\frac{9}{2}\]

Work Step by Step

\[\begin{gathered} \int_1^4 {\left( {1 - x} \right)\left( {x - 4} \right)} dx \hfill \\ \hfill \\ {\text{simplify the}}\,\,{\text{integrand}} \hfill \\ \hfill \\ \int_1^4 {\left( {5x - {x^2} - 4} \right)} dx \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ \left( {\frac{{5{x^2}}}{2} - \frac{{{x^3}}}{3} - 4x} \right)_1^4 \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ \left( {\frac{{5{{\left( 4 \right)}^2}}}{2} - \frac{{{{\left( 4 \right)}^3}}}{3} - 4\left( 4 \right)} \right) - \left( {\frac{{5{{\left( 1 \right)}^2}}}{2} - \frac{{{{\left( 1 \right)}^3}}}{3} - 4\left( 1 \right)} \right) \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ \frac{8}{3} + \frac{{11}}{6} \hfill \\ \hfill \\ \frac{9}{2} \hfill \\ \end{gathered} \]
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