Calculus (3rd Edition)

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

Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.2 Fluid Pressure and Force - Exercises - Page 475: 22


$$595350 \mathrm{N}$$

Work Step by Step

Since $$ \frac{\Delta y}{\sin 30^{\circ}}=2 \Delta y $$ and the area of each strip is $$ A=(3)(2)(\Delta y)=6 \Delta y $$ Therefore, \begin{aligned} F=\rho g \int_{a}^{b} y f(y) d y &=9800 \int_{6}^{7.5} 6 y d y \\ &=9800\left[3 y^{2}\right]_{6}^{7.5} \\ &=9800[168.75-108] \\ &=9800[60.75] \\ &=595350 \mathrm{N} \end{aligned}
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