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: 77



Work Step by Step

Recall that $(e^x)'=e^x$ Let $ u= -x^{2}/2$, then $ du=-xdx $ and $ u $ takes the values from $0$ to $-1/2$ and hence we have $$ \int_0^1 xe^{ -x^{2}/2} dx=-\int_0^{-1/2} e^{ u} du\\ =-\left[e^{u}\right]_0^{-1/2}=-(e^{-1/2}-1)=1-e^{-1/2} . $$
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