Need help with integration application!

[Daved26]

The width of a ship,s deck is measured every 30 feet and has the following measurements, in feet:
5.5, 34, 53.5, 57.2, 61, 59.4, 59, 56.8, 45.2, 32.6, 12
Approximate the area of the ships deck using trapezoidal rule and simpsons rule

I know the rules are as follows: trapezoidal rule = (delta x)/2 [f(x₀)+2f(x₁)+2f(x₂)+...f(x_n)]
simpsons rule = (delta x)/3 [f(x₀)+4f(x₁)+2f(x₂)+...f(x_n)]
delta x = (b-a)/n
I am just not sure how to set it up, once i have that i will be able to solve easily i think

 

[HallsofIvy]

The width of a ship,s deck is measured every 30 feet and has the following measurements, in feet:
5.5, 34, 53.5, 57.2, 61, 59.4, 59, 56.8, 45.2, 32.6, 12
Approximate the area of the ships deck using trapezoidal rule and simpsons rule

I know the rules are as follows: trapezoidal rule = (delta x)/2 [f(x₀)+2f(x₁)+2f(x₂)+...f(x_n)]
simpsons rule = (delta x)/3 [f(x₀)+4f(x₁)+2f(x₂)+...f(x_n)]
delta x = (b-a)/n
I am just not sure how to set it up, once i have that i will be able to solve easily i think

Have you drawn a picture? That might help. But you should know that if the "height" of a region is given by f(x) then the area is given by \(\displaystyle \int f(x)dx\). So here you are asked to use the trapezoidal rule and Simpson's rule to integrate f(x) with f(0)= 5.5, f(30)= 34, f(60)= 53.5, etc. Do you see where I got the "0, 30, 60", etc.?

So what is delta x? What are \(\displaystyle f(x_0)\), \(\displaystyle f(x_1)\), etc.? And what is "n"?

 

[Daved26]

I actually ended up solving it on my own, but i appreciate the time you took to respond. Thanks!!