Practice question · Select all that apply
Select every statement about numerical integration that is TRUE.
Hints
- Two options are contradicted directly by the lesson's pitfall and by its definitions.
- Which rule fits lines and which fits parabolas?
Show the answer
- A. A higher-order rule reaches a given accuracy at a larger step size than a low-order one
- B. Numerical integration is needed when no closed-form antiderivative exists
- D. Simpson's rule is exact for a cubic polynomial
Why
Simpson's is exact through degree three, quadrature exists precisely for integrals with no antiderivative, and higher order buys accuracy at coarser grids. Unlimited refinement is defeated by round-off, and it is Simpson's rule, not the trapezoidal, that uses parabolas.
Practise Numerical Integration
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