Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.9 Numerical Integration - Preliminary Questions - Page 457: 2

Answer

$T_{N}$ overestimates the value of the integral when the intergrand is concave up, thus, $T_{N}$ will overestimate the integral of y = g(x). On the other hand, $M_{N}$ overestimates the value of the integral when the integrand is concave down, thus $M_{N}$ will overestimate the integral of y = f(x)

Work Step by Step

$T_{N}$ overestimates the value of the integral when the intergrand is concave up, thus, $T_{N}$ will overestimate the integral of y = g(x). On the other hand, $M_{N}$ overestimates the value of the integral when the integrand is concave down, thus $M_{N}$ will overestimate the integral of y = f(x)
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