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The accuracy of the trapezoidal rule is influenced by several factors, including:

  1. Function Behavior: The smoothness and continuity of the function being integrated; functions with more curves may lead to greater error.
  2. Interval Width: The size of the subintervals; smaller intervals generally yield more accurate results.
  3. Number of Subintervals: Increasing the number of trapezoids improves accuracy, as it better approximates the area under the curve.
  4. Endpoints: The choice of endpoints can affect the approximation, particularly if the function has significant variation near the edges.
  5. Higher Derivatives: The presence and magnitude of higher derivatives of the function can also impact the error; functions with large second derivatives can produce greater inaccuracies.
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1mo ago

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