Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 4 - Integration - Page 274: 45

Answer

Lower estimate: $-48$ Upper estimate: $88$

Work Step by Step

If f is decreasing, the maximum of each subinterval is at the left end , and the minimum is at the right. $\begin{array}{lll} subinterval & minimum & maximum\\ [0,2] & 24 & 32\\ [2,4] & 12 & 24\\ [4,6] & -4 & 12\\ [6,8] & -20 & -4\\ [8,10] & -36 & -20 \end{array}$ Subinterval width: $2.$ Lower estimate: $[24+12-4-20-36](2)=-48$ Upper estimate: $[32+24+12-4-20](2)=88$
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