The trapezoidal rule for integration gives an exact result when the integrand…
2002
The trapezoidal rule for integration gives an exact result when the integrand is a polynomial of degree:
- A.
0 but not 1
- B.
1 but not 0
- C.
0 or 1
- D.
2
Show answer & explanation
Correct answer: C
The trapezoidal rule replaces the integrand over each interval by the straight line joining the endpoint values. This approximation is exact whenever the integrand itself is a straight-line function. Therefore it is exact for constant polynomials (degree 0) and linear polynomials (degree 1), but not generally for degree 2. Hence the answer is 0 or 1.