University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises: 35

Answer

$\frac{1}{2}\cdot[{e^1}-1]\approx 0.8591 $,

Work Step by Step

Let $u=x^2$, therefore $\frac{du}{dx}=2x$, therefore$\int_{0}^{1} (x\cdot e^{x^2}) dx=\frac{1}{2}\cdot{ \int_{0}^{1} (e^u}) du=\frac{1}{2}\cdot[{e^u}]_{0}^{1}=\frac{1}{2}\cdot[{e^1}-e^0]=\frac{1}{2}\cdot[{e^1}-1]\approx 0.8591 $,
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