Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 288: 56


$\approx 0.824$

Work Step by Step

The area of under $y=f(x)$ over an interval $[m,n]$ about the x-axis is given by: $Area, A= \int_{0.83}^{\pi} (\sin x -(1-\dfrac{x}{\pi})) \ dx \\ = \int_{0.83}^{\pi} [\sin x -1+\dfrac{x}{\pi})] \ dx \\=[-\cos x -x+\dfrac{x^2}{2 \pi}]_{0.83}^{\pi}$ Now, we will use a graphing calculator to obtain the approximate value of the area. So, $Area, A \approx 0.824$
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