Calculus (3rd Edition)

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

Chapter 5 - The Integral - 5.2 The Definite Integral - Exercises - Page 246: 65



Work Step by Step

Since $$\int_{1}^{b} f(x) d x =1-b^{-1} $$ Then \begin{align*} \int_{1}^{6}(3 f(x)-4) d x&=3 \int_{1}^{6} f(x)-\int_{1}^{6} 4 d x\\ &=3\left(1-6^{-1}\right)-4(6-1)\\ &=3\left(1-\frac{1}{6}\right)-4(5)\\ &=3\left(\frac{5}{6}\right)-20\\ &=\frac{5}{2}-20\\ &=-\frac{35}{2} \end{align*}
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