Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 461: 99


$$ 0.74805$$

Work Step by Step

Given $$\int_{0}^{1} e^{-x^{2}} d x $$ We have: $\Delta x=\dfrac{b-a}{n}=\dfrac{1}{5}=0.2$ Therefore, the midpoints of these sub-intervals are $$\{0.1,0.3,0.5,0.7,0.9\}$$ Hence \begin{align*} M_{n}&= \sum_{i=1}^{n}f(m_i)\Delta x\\ M_{5}&= \left[ f(m_1)+ f(m_2)+ ..+f(m_5)\right]\Delta x\\ &=(0.2)\left[ f(0.1)+ f(0.3)+ f(0.5)+ f(0.7)+ f(0.9)\right]\\ &\approx 0.74805 \end{align*}
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