Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 78


$\frac{1}{6}(e^{12}-1) $

Work Step by Step

Let $ u= 3y^2$, then $ du=6ydy $ and $ u $ takes the values from $0$ to $12$; hence we have $$ \int_0^2 ye^{ 3y^2} dy=\frac{1}{6}\int_0^{12} e^{ u} du\\ =\frac{1}{6}\left[e^{u}\right]_0^{12}=\frac{1}{6}(e^{12}-1) . $$
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