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: 103


$$ 0.7468$$

Work Step by Step

Given $$\int_{0}^{1} e^{-x^{2}} d x $$ Since $\Delta x=\dfrac{b-a}{n}=\dfrac{1}{4}=0.25$ , then by using Simpson’s rule, we get \begin{align*} S_{n}&=\dfrac{\Delta x}{3}\left[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)..+4f(x_{n-1})+f(x_n)\right]\\ S_{4}&=\dfrac{\Delta x}{3}\left[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+ f(x_{4}) \right] \\ &=\dfrac{1}{12}\left[f(0)+4f(0.25)+2f(0.5)+4f(0.75)+ f(1) \right]\\ &\approx 0.7468 \end{align*}
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