Have you fitted a polynomial to your data yet to find the function ?
A rectangular swimming pool is 30 ft wide and 50 ft long. The table below shows the depth h(x) of the water at 5-ft intervals from one end of the pool to the other. Estimate the volume of water in the pool using the Trapezoidal rule with n=10, applied to the integral .
I have to use the trapezoidal rule to solve this, and it all seems confusing, but probably isn't. Any help is appreciated, thanks. The 5 in the integral is suppose to be a 50, but I couldn't get the latex to work right -.-
I don't see why you would need to fit a polynomial to your data. The whole point of the trapezoid rule is to use discrete points to estimate the integral, and you've been given your points already.
Try plotting the depth versus the distance from the end of the pool and connecting each point to the next one by a line segment. Those will be your 10 trapezoids.
You got the same answer because that's all they wanted you to do. The problem was just testing whether you could go through the steps of the trapezoid approximation.
Fitting a polynomial to those points could give a more accurate answer if this was a "real world" problem, or it could be a disaster. It's easy to find a bunch of points that are practically collinear, but when you plot the polynomial through them it looks nothing like the real data.
But if you really want to know how to fit a polynomial to data, it just reduces to solving a system of linear equations. For example, to get a parabola through the points (1,2), (2,3), and (3, 8), you would solve
(let's see how my first attempt at latex on this forum goes). Obviously for 11 points you'll want to use a computer.
edit: Just to clarify, when I say "the" polynomial I mean the interpolating polynomial that goes through every point. A lower degree polynomial that approximates the data may work well, but that's kind of overthinking the problem.