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 462: 105


$$ V\approx 20~\text{acre ft} =871,200 \text{ ft}^3 $$

Work Step by Step

Since $$V=\int_{0}^{18} A(h) d h$$ From the given table, $\Delta x=2$. Then, by using $T_9$, we get \begin{align*} T_{n}&=\dfrac{1}{2}\left[f(x_0)+2f(x_1)+2f(x_2)+..+2f(x_{n-1})+f(x_n)\right]\Delta x\\ T_{9}&= \left[f(x_0)+2f(x_1)+2f(x_2)+\cdots+2f(x_{8})+f(x_9)\right]\Delta x\\ &= \left[f(0)+2f(2)+2f(4)+2f(6)+2f(8)+2f(10)+2f(12)+2f(14)+2f(16)+f(18)\right] \\ &\approx 20 \text{arce ft} \end{align*} Hence $$ V\approx 20~ \text{acre ft} =871,200 \text{ ft}^3 $$
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