Mathematics · Riemann Integration
Let f: [0, 1] → &mathbb{R} be a continuous function. For any partition P of [0, 1], let L(P, f) and U(P, f) be the lower and upper Darboux sums, respectively. If P = {0, 1/10, 2/10, ..., 1} and Q = {0, 1/100, 2/100, ..., 1}, then which of the following relations is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1L(P, f) ≤ L(Q, f) ≤ U(Q, f) ≤ U(P, f)✓
- 2L(P, f) ≤ L(Q, f) and U(P, f) ≤ U(Q, f)
- 3L(Q, f) ≤ L(P, f) and U(Q, f) ≤ U(P, f)
- 4L(Q, f) ≤ L(P, f) ≤ U(P, f) ≤ U(Q, f)
Correct answer
L(P, f) ≤ L(Q, f) ≤ U(Q, f) ≤ U(P, f)
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