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theBEAST
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Homework Statement
The Attempt at a Solution
Thus my answer is N = 20.
I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?
Trapezoidal Approximation Error
- Thread starter theBEAST
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- Approximation Error
In summary, Trapezoidal Approximation Error is a numerical error that occurs when using the trapezoidal rule to approximate the value of a definite integral. It is calculated by taking the absolute value of the difference between the exact value of the integral and the value obtained using the trapezoidal rule. The size of the error can be affected by the number of subintervals used and the shape of the function being integrated. To reduce the error, one can increase the number of subintervals or use a different numerical integration method. However, Trapezoidal Approximation Error has limitations as it is only an approximation and does not account for sharp changes in the function.
Thus my answer is N = 20.
I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?
- #2
Mark44
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theBEAST said:Homework Statement
The Attempt at a Solution
Thus my answer is N = 20.
I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?
Your work looks fine to me, but I think I would use < instead of ≤. If your error < .005, you'll be guaranteed 2 decimal place accuracy.
Related to Trapezoidal Approximation Error
What is Trapezoidal Approximation Error?
Trapezoidal Approximation Error is a type of numerical error that occurs when using the trapezoidal rule to approximate the value of a definite integral. It is the difference between the exact value of the integral and the value obtained using the trapezoidal rule.
How is Trapezoidal Approximation Error calculated?
Trapezoidal Approximation Error is calculated by taking the absolute value of the difference between the exact value of the integral and the value obtained using the trapezoidal rule. It is often expressed as a percentage of the exact value.
What factors can affect the size of Trapezoidal Approximation Error?
The size of Trapezoidal Approximation Error can be affected by the number of subintervals used in the trapezoidal rule, as well as the shape of the function being integrated. In general, using more subintervals will decrease the error, while using a function with a steep curve or large fluctuations can increase the error.
How can Trapezoidal Approximation Error be reduced?
Trapezoidal Approximation Error can be reduced by increasing the number of subintervals used in the trapezoidal rule. This will result in a more accurate approximation of the integral. Additionally, using a different numerical integration method, such as Simpson's rule, can also reduce the error.
What are the limitations of Trapezoidal Approximation Error?
Trapezoidal Approximation Error is only an approximation and will never be completely accurate. It also assumes that the function being integrated is continuous and does not take into account any sharp changes in the function. Additionally, the error can become very large if the function has a steep curve or large fluctuations.
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