Question

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of 2∫1 f(x) dx .
x 1 1.1 1.3 1.6 1.7 1.8 2.0
f(x) 1 3 5 8 10 11 14

Answer 1

Just add up the values. I assume you know how to find the area of a trapezoid.
(f(1.0)+f(1.1))/2 * (1.1-1.0) +...+(f(1.8)+f(2.0))/2 * (2.0-1.8)

Too bad they didn't use equal widths. Then the sum would have been much easier:
1/6 (f(1) + 2*f(7/6) + ... + 2*f(11/6) + f(2))

Answer 2

slight oversight I think
(1/2)(1/6) [ f(1) + 2 f(7/6) etc

Answer 3

( I am a Naval Architect :)

Answer 4

nice catch. I originally included the 1/2, but then I noticed that the widths were not all the same, and in my PS I left it out.

But I'm sure William picked right up on that... ... ...