Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 390: 36

Answer

$$4$$

Work Step by Step

$$\eqalign{ & \int_0^{\ln 16} {{e^{x/4}}} dx \cr & {\text{use the formula }}\int_a^b {{e^{kx}}} dx = \left( {\frac{{{e^{kx}}}}{k}} \right)_a^b;{\text{ for this exercise set }}k = 1/4 \cr & \int_0^{\ln 16} {{e^{x/4}}} dx = \left( {\frac{{{e^{x/4}}}}{{1/4}}} \right)_0^{\ln 16} \cr & = 4\left( {{e^{x/4}}} \right)_0^{\ln 16} \cr & {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 281}}} \right) \cr & = 4\left( {{e^{\left( {\ln 16} \right)/4}}} \right) - 4\left( {{e^{0/4}}} \right) \cr & = 4\left( {{e^{\left( {\ln {{16}^{1/4}}} \right)}}} \right) - 4\left( {{e^0}} \right) \cr & {\text{simplifying}} \cr & = 4\left( {{e^{\ln 2}}} \right) - 4\left( 1 \right) \cr & = 4\left( 2 \right) - 4 \cr & = 4 \cr} $$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.