Estimating Pool Area Using Simpson's Rule

• bns1201
In summary, The conversation discusses using Simpson's Rule to estimate the area of a kidney-shaped swimming pool, with measurements at 2 meter intervals. The answer should be rounded to the nearest square meter.
bns1201
I put this in the homework section a few days ago, but the homework was already due, and I'd like an explanation as to how to do this please. I have a feeling a similar problem will be on the exam.

The widths (in meters) of a kidney-shaped swimming pool were measured at 2 meter intervals as indicated in the figure. Use Simpson's Rule to estimate the area of the pool. Please round the answer to the nearest square meter.

a = 5.8
b = 6.6
c = 5.4
d = 5.8
e = 5.2
f = 4.8
g = 5.2

Thanks

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I am assuming that a and g were each 2 meters from the edge.
Then Simpson's rule gives 4(4a+2b+4c+2d+4e+2f +4g)/6.

Last edited:

1. What is Simpsons Rule and how does it work?

Simpsons Rule is a numerical method used to approximate the area under a curve. It works by dividing the area into smaller segments and using a quadratic polynomial to estimate the area of each segment, then summing them together to get the overall approximation.

2. When is Simpsons Rule typically used?

Simpsons Rule is typically used when the function being integrated is difficult to integrate analytically or when the interval of integration is too large to use other numerical methods such as the Trapezoidal Rule.

3. How accurate is Simpsons Rule compared to other numerical methods?

Simpsons Rule is generally more accurate than the Trapezoidal Rule and other numerical methods. With an appropriate number of segments, Simpsons Rule can provide an estimation that is within 0.1% of the actual area under the curve.

4. Can Simpsons Rule be used for all types of functions?

No, Simpsons Rule is only applicable to functions that are smooth and continuous over the interval of integration. If the function has discontinuities, sharp turns, or is not continuous, Simpsons Rule will not provide an accurate approximation.

5. What is the formula for Simpsons Rule?

The formula for Simpsons Rule is:

where h is the width of each segment and n is the number of segments. The function f(x) represents the equation of the curve being integrated.

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