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: 31

Answer

\[\frac{7}{6}\]

Work Step by Step

\[\begin{gathered} \int_0^1 {\left( {x + \sqrt x } \right)} dx \hfill \\ \hfill \\ {\text{ radical property }}\sqrt x = {x^{1/2}} \hfill \\ \hfill \\ \int_0^1 {\left( {x + {x^{1/2}}} \right)} dx \hfill \\ \hfill \\ {\text{Integrate using the rule }}\int {{x^n}} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ \hfill \\ \left[ {\frac{{{x^{1 + 1}}}}{{1 + 1}} + \frac{{{x^{1/2 + 1}}}}{{1/2 + 1}}} \right]_0^1 \hfill \\ \hfill \\ \left[ {\frac{{{x^2}}}{2} + \frac{{{x^{3/2}}}}{{3/2}}} \right]_0^1 \hfill \\ \hfill \\ \left[ {\frac{{{x^2}}}{2} + \frac{2}{3}{x^{3/2}}} \right]_0^1 \hfill \\ \hfill \\ {\text{Fundamental Theorem of calculus}} \hfill \\ \hfill \\ \left[ {\frac{{{{\left( 1 \right)}^2}}}{2} + \frac{2}{3}{{\left( 1 \right)}^{3/2}}} \right] - \left[ {\frac{{{{\left( 0 \right)}^2}}}{2} + \frac{2}{3}{{\left( 0 \right)}^{3/2}}} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ \frac{1}{2} + \frac{2}{3} \hfill \\ \hfill \\ \frac{7}{6} \hfill \\ \end{gathered} \]
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