Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.1 Basic Approaches - 7.1 Exercises: 12

Answer

\[ = 2\]

Work Step by Step

\[\begin{gathered} \int\limits_{ - 5}^0 {\frac{{dx}}{{\sqrt {4 - x} }}} \hfill \\ \hfill \\ set\,\,4 - x = u\,\,then - dx = du\,\,\,or\,\,dx = - du \hfill \\ \hfill \\ lower\,\,li\,mit\,\, = \,4 - \,\left( { - 5} \right) = 9 \hfill \\ \hfill \\ upper\,\,\,li\,mit\, = \,4 - 0 = 4 \hfill \\ \hfill \\ integral\,\,becomes \hfill \\ \hfill \\ \int\limits_{ - 5}^0 {\frac{{dx}}{{\sqrt {4 - x} }}} = - \int\limits_9^4 {\frac{{du}}{{\sqrt u }}} \hfill \\ \hfill \\ integrate\,\,\,and\,evalute \hfill \\ \hfill \\ = - 2\,\,\,\left[ {\sqrt u } \right]_9^4 \hfill \\ \hfill \\ = - 2\,\left( {2 - 3} \right) \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ = 2 \hfill \\ \end{gathered} \]
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