Chapter 8 - Further Applications of Integration - 8.3 Applications to Physics and Engineering - 8.3 Exercises - Page 605: 3

$7000$ lbs

Here, $A_i=2 \triangle x $ The depth of the plate is from $x=3$ to $x=3+8=11m $ and $F_i=P_iA_i=62.5 \times x_i \times 2 \triangle x $ Thus, $F=\lim\limits_{n \to \infty} \Sigma_{i=1}^n 62.5(x_i) \times 2 dx $ This gives: $F=(2) \int_3^{11} 62.5(x_i) \times 2 dx $ and $F=(62.5) |x^2|_3^{11}=62.5 \times (121-9)=7000$ lbs